Exam 4: Exponential and Logarithmic Functions

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. - $8 + 3 \ln x = 6$

Solve the equation by expressing each side as a power of the same base and then equating exponents. - $3 x = 27$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( \frac { x y ^ { 5 } } { z ^ { 9 } } \right)$

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

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. - $5 \ln a - 8 \ln b$

Evaluate the expression without using a calculator. - $\ln \frac { 1 } { e ^ { 2 } }$

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. - $2 \log _ { x } 4 + \log _ { x } 3$

Graph the function -Use the graph of $f ( x ) = 3 ^ { x }$ to obtain the graph of $g ( x ) = - 3 ^ { x }$ .

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. - $\log _ { 3 } x = 4$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 3 } \left( \frac { 81 } { \sqrt { x - 1 } } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \sqrt [ 3 ] { \mathrm { ey } }$

Graph the function -Use the graph of $f ( x ) = e ^ { x }$ to obtain the graph of $g ( x ) = e ^ { x + 4 }$ .

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. - $\log _ { 4 } ( x - 3 ) = - 3$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $5 ^ { x + 7 } = 2$

Approximate the number using a calculator. Round your answer to three decimal places. -A sample of $400 \mathrm {~g}$ of lead-210 decays to polonium-210 according to the function given by $\mathrm { A } ( \mathrm { t } ) = 400 \mathrm { e } ^ { - 0.032 \mathrm { t } }$ , where $\mathrm { t }$ is time in years. What is the amount of the sample after 30 years (to the nearest g)?

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $e ^ { 4 x } = 6$

Evaluate or simplify the expression without using a calculator. -Use the formula $R = \log \left( \frac { a } { T } \right) + B$ to find the intensity $R$ on the Richter scale, given that amplitude a is 431 micrometers, time T between waves is $2.4$ seconds, and B is $2.4$ . Round answer to one decimal place.

Find the domain of the logarithmic function. - $f ( x ) = \log \left( \frac { x + 6 } { x - 4 } \right)$

Solve the exponential equation. Express the solution set in terms of natural logarithms. - $\mathrm { e } ^ { 5 \mathrm { x } } = 8$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 6 } \left( \frac { 2 } { 5 } \right)$