Exam 9: Exponential and Logarithmic Functions

The __________ line test can be used to decide whether the graph of a function represents a one-to-one function.

Solve the equation. Express the answer to four decimal places. $\ln x = 1.1563$ $x =$ __________

Find the db gain of an amplifier if the input voltage is 0.71 volts when the output voltage is 30 volts.

Evaluate the expression. $\log _ { 5 } 9$

$f ( x ) = 3 ^ { x }$ is an example of a(n) __________ function.

Evaluate the expression. $\ln e ^ { 5 }$

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that q , w and r are positive numbers. $\log _ { 5 } 9$

Let $f ( x ) = 5 x - 9$ and $g ( x ) = 4 x - 2$ . Find the domain of $\frac { f } { g }$ .

Write the logarithmic expression as one logarithm. Assume that h , j , and k are positive numbers. $- 4 \log h - 5 \log j + \log k$

$\log _ { b } x$ is the _________ to which b is raised to get x .

An equation with a variable in its exponent, such as ${ } ^ { 227 } \mathrm { Th }$ , is called a(n) __________ equation.

The __________ of f and h , denoted as $f \cdot h$ , is defined by $( f \cdot h ) ( x ) =$ __________ and the __________ of $f$ and $h$ , denoted as $\frac { f } { h }$ , is defined by $\left( \frac { f } { h } \right) ( x ) =$ __________.

Solve the equation. $\log ( x - 5 ) - \log ( x - 2 ) = \log \frac { 4 } { x }$ If there is more than one solution, separate your answers with commas.

The functions $f ( x ) = \log _ { 6 } x$ and $g ( x ) = 6 ^ { x }$ are __________ functions.

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that q , w , r and a are positive numbers, and $\log _ { 5 } 9$ . $\log _ { b } 7 = 0.8451$

Write the exponential equation as a logarithmic equation. $\left( \frac { 1 } { 2 } \right) ^ { - 5 } = 32$

Evaluate: $\log _ { 8 } \left( \log _ { 2 } \left( \log _ { 3 } 9 ^ { 2 } \right) \right)$

Solve the equation. $6 ^ { 4 x } = \frac { 1 } { 216 }$ If there is more than one solution, separate your answers with commas.

An initial deposit of $10,000 earns 16% interest, compounded monthly. How much will be in the account after 10 years? Please give the answer to the nearest cent. $__________

An initial investment of $5,100 earns 8.5% interest, compounded continuously. What will the investment be worth in 12 years?