Exam 4: Exponential and Logarithmic Functions

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log \left[ \frac { 8 x ^ { 4 } \sqrt [ 4 ] { 5 - x } } { 3 ( x + 5 ) ^ { 2 } } \right]$

Solve the problem. -The size of the bear population at a national park increases at the rate of $4.6 \%$ per year. If the size of the current population is 157 , find how many bears there should be in 6 years. Use the function $f ( x ) = 157 e ^ { 0.046 t }$ and round to the nearest whole number.

Use Natural Logarithms Evaluate or simplify the expression without using a calculator. - $e ^ { \ln 14 x ^ { 4 } }$

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. - $3 \log 54 + \frac { 1 } { 6 } \log 5 ( r - 7 ) - \frac { 1 } { 2 } \log 5 r$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $2 ( 1 + 2 x ) = 32$

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. - $4 \log _ { b } y + 3 \log _ { b } z$

Graph the function. -Use the graph of $\log _ { 2 } x$ to obtain the graph of $f ( x ) = \log _ { 2 } ( x + 2 )$ .

Graph the function. -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { 6 x }$ .

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 9 } \left( x ^ { 2 } - 8 x \right) = 1$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { x - 4 } { x ^ { 4 } } \right)$

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log ( 2 + x ) - \log ( x - 2 ) = \log 3$

Graph the function. - $f(x)=2^{x} \text { and } g(x)=\log _{2} x$

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 35 } ( x - 2 ) = 1 - \log _ { 35 } x$

Use the Power Rule Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } x ^ { 6 }$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $8 ( x - 10 ) / 6 = \sqrt { 8 }$

Evaluate the expression without using a calculator. - $\log _ { 12 } 1$

Use the One-to-One Property of Logarithms to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 7 } x ^ { 2 } = \log _ { 7 } ( 5 x + 36 )$

Use the Definition of a Logarithm to Solve Logarithmic Equations Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. - $\log _ { 4 } ( x + 2 ) - \log _ { 4 } x = 2$

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = \log x - 1$ .

The graph of a logarithmic function is given. Select the function for the graph from the options. -