Exam 9: Exponential and Logarithmic Functions

Graph the function and its inverse on the same set of axes. - $y = \log _ { 2 } x ; y = 2 ^ { x }$

Solve the equation. - $\left( \frac { 1 } { 4 } \right) ^ { x } = 8 ^ { 2 - x }$

Find the value of the logarithmic expression. - $\log _ { 11 } 1$

Solve. -Use the formula $R = \log \left( \frac { \mathrm { a } } { \mathrm { T } } \right) + \mathrm { B }$ to find the intensity $\mathrm { R }$ on the Richter scale, given that amplitude a is 438 micrometers, time T between waves is $3.1$ seconds, and B is 3.1. Round answer to one decimal place.

Solve. Round the answer to the nearest whole. -If the annual population growth rate is 5.2%, find how long will it take a population of birds to increase from 400 birds to 1100 birds.

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal -The of functions f and g is (f $( f \circ g ) ( x ) = f ( g ( x ) )$

Approximate the logarithm to four decimal places using the change of base formula. - $\log _ { 5 }$

Find the inverse of the one-to-one function. - $f ( x ) = \sqrt [ 3 ] { x - 8 }$

Find f(x) and g(x) so that the given function h(x) = (f ° g)(x). - $h ( x ) = \sqrt [ 3 ] { x + 4 }$

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 4 } x - \log _ { 4 } ( x + 6 ) + \log _ { 4 } \left( x ^ { 2 } - 6 \right)$

Write as a logarithmic equation. - $\mathrm { e } ^ { 8 } = \mathrm { x }$

Graph the functions on the same set of axes. - $y=4^{x} ; y=\log _{4} x$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\ln x = 0.3$

f(x)=x+7 ; g(x)=5x - 2 Find (f+g)(x) .

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log 17 x = 1.4$

Decide whether the statement is true or false. - $\frac { \log _ { 5 } 150 } { \log _ { 5 } 30 } = 1$

Use the following approximations to find the approximate value of the logarithmic expression: $\log _ { b } 3 \approx 0.5$ logb $8 \approx 0.9$ $\log _ { b } 5 \approx 0.7$ logb $20 \approx 1.3$ - $\log _ { b } \sqrt [ 3 ] { 8 }$ Round answer to nearest hundredth.

Provide an appropriate response. -Write the expression $\log _ { 7 } \frac { 3 x } { y ^ { 2 } }$ as a sum or difference of logarithms.

Determine whether the graph of the function is the graph of a one-to-one function. -

Determine whether the graph is the graph of a one-to-one function. -