Exam 5: Inverse, Exponential, and Logarithmic Functions

The logarithmic functio $f ( x ) = - 100 + 87 \ln x$ ln x models the number of visitors (in millions) to a certain country's museums, where x is the number of years since the initial recording of the number of visitors. Use this function To estimate the number of visitors in year 60. Round to the nearest tenth of a year.

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes. - $f ( x ) = \frac { 2 } { x }$

Give the answer in exact form. - $3 ^ { 2 x } - 3 \left( 3 ^ { x } \right) = 40$

Find the number of years for $14,100 to grow to $16,600 at 3% compounded semiannually. Round to the nearest tenth of a year.

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $\text { Let } f ( x ) = 4 ^ { x } \text {. Find } \left( \frac { 5 } { 2 } \right) \text {. }$

Solve for the indicated variable. - $\mathrm { P } = 50,000 \cdot \mathrm { e } ^ { \mathrm { s } / 4 }$ , for $\mathrm { s }$

Determine whether or not the function is one-to-one. - $f ( x ) = \sqrt [ 3 ] { 2 x + 9 }$

For the function as defined that is one-to-one, graph f and $\mathrm { f } ^ { - 1 }$ on the same axes. - $f(x)=x^{2}+5$

Write in logarithmic form. - $16 ^ { 3 / 4 } = 8$

Use properties of logarithms to evaluate the expression. - $100 ^ { \log _ { 10 } 3 }$

Solve the equation and express the solution in exact form. - $\log _ { 4 } ( x + 1 ) + \log _ { 4 } ( x - 1 ) = 2$

Write an equivalent expression in exponential form. - $\log _ { 4 } x = 3$