Exam 9: Exponential and Logarithmic Functions

Evaluate: $\ln \frac { 1 } { e ^ { 3 } }$

What is the domain of the function $f ( x ) = e ^ { x }$ ?

Solve: $\log _ {x } 81 = 4$

Let $f ( x ) = 5 x - 5 \text { and } g ( x ) = - 2 x + 9$ . Find: $( f - g ) ( 3 )$ .

How long will it take $1000 to double if it is invested at an annual rate of 6% compounded continuously? Please round the answer to one decimal place. __________ yr

The population of North Rivers is decreasing exponentially according to the formula $P = 3997 ( 0.94 ) ^ { t }$ , where $t$ is measured in years from the present date. Find the population in 7 years, 8 months. Please round the answer to the nearest integer.

Evaluate the expression. $\log _ { 4 } 4 ^ { 2 }$

Refer to the graph of $f ( x ) = 2 ^ { x }$ . What is the range of the function? Please enter your answer in interval notation.

Solve for x . $\log _ { x } \frac { 64 } { 49 } = 2$

Evaluate: $\log _ { 7 } \sqrt { 7 }$

The functions $f \text { and } f ^ { - 1 }$ are __________.

Write the logarithmic expression as one logarithm. Assume that u and i are positive numbers. $2 \log u + \frac { 1 } { 2 } \log i$

If $500 is deposited in an account paying 8.3% annual interest, compounded semiannually, how long will it take for the account to increase to $850? Please round the answer to the nearest tenth. __________ years

Find the inverse of the function and express it using $f ^ { - 1 } ( x )$ notation. $f ( x ) = x ^ { 3 } - 6$

Compare the graph of $f ( x ) = 6 ^ { x - 5 }$ to the graph of $y = 6 ^ { x }$ .

An equation with a logarithmic expression that contains a variable, such as ${ } ^ { 227 } \mathrm { Th }$ , is a(n) __________ equation.

Evaluate: $\log _ { 8 } \left( \log _ { 2 } \left( \log _ { 4 } 256 \right) \right)$

Let $f ( x ) = 7 x - 6 \text { and } g ( x ) = - 2 x + 2$ . Find: $f + g$

To find $\ln e ^ { 9 }$ , we ask, To what power must we raise __________ to get $e ^ { 9 }$ ? Since the answer is the 9th power, $\ln e ^ { 9 } =$ __________.