Exam 5: Inverse, Exponential, and Logarithmic Functions

Round your answer to the nearest tenth, when appropriate. Use the formula $\mathrm { pH } = - \log \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right]$ , as needed. -Find the $\mathrm { pH } \text { if } \left[ \mathrm { H } _ { 3 } \mathrm { O } ^ { + } \right] = 6.7 \times 10 ^ { - 5 }$

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = 6 x ^ { 2 } - 9 , x \geq 0$

Write an equivalent expression in exponential form. - $\log _ { 4 } \left( \frac { 1 } { 16 } \right) = - 2$

Solve the equation and express the solution in exact form. - $\log ( x + 10 ) = 1 + \log ( 4 x - 3 )$

Between what two integers does the solution of log7 $x = 1.56$ lie?

Round to the nearest thousandth. - $183 ( 1.88 ) ^ { x / 3 } = 366$

Write an equivalent expression in exponential form. - $x = \log _ { 5 } \sqrt [ 5 ] { 25 }$

Evaluate the logarithm. - $\log _ { 10 } 100$

Find the function value. If the result is irrational, round your answer to the nearest thousandth. - $f ( x ) = \left( \frac { 1 } { 2 } \right) ^ { x }$

Find the required annual interest rate, to the nearest tenth of a percent, for $5100 to grow to $6300 if interest is compounded quarterly for 5 years.

Solve the equation. -

If the function is one-to-one, find its inverse. If not, write "not one-to-one." - $f ( x ) = \sqrt [ 3 ] { x + 3 }$

Give the answer in exact form. - $4 \mathrm { e } ^ { 2 \mathrm { x } } + 9 \mathrm { e } ^ { \mathrm { x } } = 9$

Match the function with its graph. - $f ( x ) = \log _ { 2 } \left( \frac { 1 } { x } \right)$

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 2 } - 7 ; x \geq 0$

The loudness of a sound can be quantified in units called decibels, where the number of decibels d is given by the formula $\mathrm { d } = 10 \log \frac { \mathrm { I } } { \mathrm { I } _ { 0 } }$ What is the decibel rating of a sound having an intensity $\mathrm { I } = 1000 \mathrm { I } 0$ ?

Evaluate the logarithm. - $\log _ { 1 / 3 } 3$

An everyday activity is described. Keeping in mind that an inverse operation "undoes" what an operation does, describe each inverse activity. -opening a door

Let u = ln a and v = ln b. Write the following expression in terms of u and v without using the function ln. ln a7 B8

Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. - $\log b \sqrt { \frac { 4 x ^ { 8 } } { z ^ { 4 } } }$