Determine the correct exponential function of the form f(x) = bS1U1P1xS1S1P0 whose graph is given. -

A) $f ( x ) = 8 ^ { x }$ B) $f ( x ) = \left( \frac { 1 } { 8 } \right) ^ { x }$ C) $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$ D) $f ( x ) = 5 ^ { x }$ A) $f ( x ) = 8 ^ { x }$ B) $f ( x ) = \left( \frac { 1 } { 8 } \right) ^ { x }$ C) $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$ D) $f ( x ) = 5 ^ { x }$

Exam 5: Exponential and Logarithmic Functions and Equations

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \frac { x - 5 } { x ^ { 8 } }$

(Multiple Choice)

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Question 141

Solve the equation. - $4 ^{( 3 x - 5 )} = 256$

(Multiple Choice)

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Question 142

Solve the equation. - $\log ( 4 x ) = \log 3 + \log ( x - 2 )$

(Multiple Choice)

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Question 143

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 8 } \left( \frac { 8 } { x } \right)$

(Multiple Choice)

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Question 144

Solve the equation. - $\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4$

(Multiple Choice)

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Question 145

Graph the function. -

(Multiple Choice)

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Question 146

Graph the function. - $f(x)=\log 5 x$ $Graph the function. - f(x)=\log 5 x$

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Question 147

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $5 \log _ { 6 } 5 + \frac { 1 } { 4 } \log _ { 6 } ( r - 2 ) - \frac { 1 } { 2 } \log _ { 6 } r$

(Multiple Choice)

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Question 148

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

(Multiple Choice)

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Question 149

Evaluate the logarithm without the use of a calculator. - $\log _ { 4 } 16$

(Multiple Choice)

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Question 150

Write the exponential equation as an equation involving a logarithm. - $9 ^ { \mathrm { X } } = 81$

(Multiple Choice)

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Question 151

Graph the function. -

(Multiple Choice)

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Question 152

Solve the problem. -A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

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Question 153

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \left( \frac { \mathrm { e } ^ { 3 } } { 8 } \right)$

(Multiple Choice)

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Question 154

Solve the equation. - $3 ^ { 2 x } + 3 ^ { x } - 6 = 0$

(Multiple Choice)

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Question 155

Write the exponential equation as an equation involving a logarithm. - $5 ^ { 3 } = x$

(Multiple Choice)

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Question 156

Solve the equation. - $32 ^ { x - 1 } = 64 ^ { 3 x }$

(Multiple Choice)

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Question 157

Write the logarithmic equation as an exponential equation. - $\ln \left( \frac { 1 } { \mathrm { e } } \right) = - 1$

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Question 158

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. -ln x + ln (x + 6)= 4

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Question 159

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 4 } ( x - 3 ) - \log _ { 4 } ( x + 1 )$

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Question 160

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \frac { x - 5 } { x ^ { 8 } }$

Solve the equation. - $4 ^{( 3 x - 5 )} = 256$

Solve the equation. - $\log ( 4 x ) = \log 3 + \log ( x - 2 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 8 } \left( \frac { 8 } { x } \right)$

Solve the equation. - $\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4$

Graph the function. -

Graph the function. - $f(x)=\log 5 x$ $Graph the function. - f(x)=\log 5 x$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $5 \log _ { 6 } 5 + \frac { 1 } { 4 } \log _ { 6 } ( r - 2 ) - \frac { 1 } { 2 } \log _ { 6 } r$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Evaluate the logarithm without the use of a calculator. - $\log _ { 4 } 16$

Write the exponential equation as an equation involving a logarithm. - $9 ^ { \mathrm { X } } = 81$

Graph the function. -

Solve the problem. -A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \left( \frac { \mathrm { e } ^ { 3 } } { 8 } \right)$

Solve the equation. - $3 ^ { 2 x } + 3 ^ { x } - 6 = 0$

Write the exponential equation as an equation involving a logarithm. - $5 ^ { 3 } = x$

Solve the equation. - $32 ^ { x - 1 } = 64 ^ { 3 x }$

Write the logarithmic equation as an exponential equation. - $\ln \left( \frac { 1 } { \mathrm { e } } \right) = - 1$

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. -ln x + ln (x + 6)= 4

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 4 } ( x - 3 ) - \log _ { 4 } ( x + 1 )$

Equations, Inequalities, and Applications

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Exam 5: Exponential and Logarithmic Functions and Equations

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡3x−5x8\log _ { 3 } \frac { x - 5 } { x ^ { 8 } }log3​x8x−5​

Solve the equation. - 4(3x−5)=2564 ^{( 3 x - 5 )} = 2564(3x−5)=256

Solve the equation. - log⁡(4x)=log⁡3+log⁡(x−2)\log ( 4 x ) = \log 3 + \log ( x - 2 )log(4x)=log3+log(x−2)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - log⁡8(8x)\log _ { 8 } \left( \frac { 8 } { x } \right)log8​(x8​)

Solve the equation. - log⁡3x+log⁡3(x−24)=4\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4log3​x+log3​(x−24)=4

Graph the function. -

Graph the function. - f(x)=log⁡5x f(x)=\log 5 x f(x)=log5x

Determine the correct exponential function of the form f(x) = bx whose graph is given. -

Evaluate the logarithm without the use of a calculator. - log⁡416\log _ { 4 } 16log4​16

Write the exponential equation as an equation involving a logarithm. - 9X=819 ^ { \mathrm { X } } = 819X=81

Graph the function. -

Solve the problem. -A fossilized leaf contains 12% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon 14.

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - ln⁡(e38)\ln \left( \frac { \mathrm { e } ^ { 3 } } { 8 } \right)ln(8e3​)

Solve the equation. - 32x+3x−6=03 ^ { 2 x } + 3 ^ { x } - 6 = 032x+3x−6=0

Write the exponential equation as an equation involving a logarithm. - 53=x5 ^ { 3 } = x53=x

Solve the equation. - 32x−1=643x32 ^ { x - 1 } = 64 ^ { 3 x }32x−1=643x

Write the logarithmic equation as an exponential equation. - ln⁡(1e)=−1\ln \left( \frac { 1 } { \mathrm { e } } \right) = - 1ln(e1​)=−1

Solve the equation. Express irrational answers in exact form and as a decimal rounded to 3 decimal places. -ln x + ln (x + 6)= 4

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - log⁡4(x−3)−log⁡4(x+1)\log _ { 4 } ( x - 3 ) - \log _ { 4 } ( x + 1 )log4​(x−3)−log4​(x+1)

Equations, Inequalities, and Applications

The Rectangular Coordinate System, Lines, and Circles

Functions

Polynomial and Rational Functions

Conic Sections

Systems of Equations and Inequalities

Matrices

Sequences and Series; Counting and Probability

Math Exercises: Sets, Intervals, Absolute Value, and Properties

Filters

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \frac { x - 5 } { x ^ { 8 } }$

Solve the equation. - $4 ^{( 3 x - 5 )} = 256$

Solve the equation. - $\log ( 4 x ) = \log 3 + \log ( x - 2 )$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 8 } \left( \frac { 8 } { x } \right)$

Solve the equation. - $\log _ { 3 } x + \log _ { 3 } ( x - 24 ) = 4$

Graph the function. - $f(x)=\log 5 x$ $Graph the function. - f(x)=\log 5 x$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Evaluate the logarithm without the use of a calculator. - $\log _ { 4 } 16$

Write the exponential equation as an equation involving a logarithm. - $9 ^ { \mathrm { X } } = 81$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \left( \frac { \mathrm { e } ^ { 3 } } { 8 } \right)$

Solve the equation. - $3 ^ { 2 x } + 3 ^ { x } - 6 = 0$

Write the exponential equation as an equation involving a logarithm. - $5 ^ { 3 } = x$

Solve the equation. - $32 ^ { x - 1 } = 64 ^ { 3 x }$

Write the logarithmic equation as an exponential equation. - $\ln \left( \frac { 1 } { \mathrm { e } } \right) = - 1$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\log _ { 4 } ( x - 3 ) - \log _ { 4 } ( x + 1 )$