Exam 9: Exponential and Logarithmic Functions

Write the logarithmic expression as one logarithm. Assume that u and i are positive numbers. $\log _ { 5 } 9$

Let $f ( x ) = 4 x - 7 \text { and } g ( x ) = - 2 x + 9$ Find: $( f \cdot g ) ( 1 )$

Evaluate expression without using a calculator. $\ln e ^ { 4 }$

Solve: $\log ( x + 5 ) - \log ( x - 2 ) = \log 6$

If the function $f ( x ) = 9 x - 4$ is one-to-one, find its inverse.

Write the logarithmic expression as one logarithm. Assume that s is a positive number. $\log _ { 5 } 9$

Write the logarithmic equation as an exponential equation. $\log _ { 8 } 64 = 2$

Evaluate the expression. $\log _ { \frac { 1 } { 2 } } \frac { 1 } { 64 }$

Solve the equation. $\log x + \log ( x - 15 ) = 2$ If there is more than one solution, separate your answers with commas.

What is an asymptote of the graph?

A function is called a __________ function if different inputs determine different outputs.

Solve: $\log _ { 3 } x + \log _ { 3 } ( x - 8 ) = 2$

Write the logarithmic expression as one logarithm. Assume that h is a positive number. $\log _ { 5 } 9$

If f is a one-to-one function, the domain of f is the __________ of $f ^ { - 1 }$ , and the range of $f$ is the __________ of $f ^ { - 1 }$ .

Evaluate the expression. $\log _ { 2 } 1$

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

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify, if possible. Assume that u , i and p are positive numbers. $\log \text { uip }$

What is the domain of the function $f ( x ) = \ln x$ ? __________ What is the range of the function $f ( x ) = \ln x$ ? __________

Does ${ } ^ { 227 } \mathrm { Th }$ ?

Solve the equation. Give your answer to four decimal places. ${ } ^ { 227 } \mathrm { Th }$