Exam 9: Exponential and Logarithmic Functions

What is the x -intercept of the graph?

Use the change of base formula to identify the expression that is equivalent to $\log _ { 5 } 3$ .

If two exponential expressions with the same base are equal, their exponents are _______.

Solve the following equation. $3 ^ { x ^ { 2 } - 2 x }= 27$ If there is more than one solution, separate your answers with commas.

Determine the graph of the function is one-to-one.

Solve the equation. Give your answer to four decimal places. $5 ^ { x } = 7$ If there is more than one solution, separate your answers with commas.

Let $f ( x ) = 5 x + 4$ and $g ( x ) = x ^ { 2 } - 3$ . Find the composition. $( g \circ f ) ( x )$

Solve: $\log _ { 32 } x = \frac { 2 } { 5 }$

Like $\pi$ , the number e is a(n) __________ number.

The population of the earth is approximately 6.1 billion people and is growing at an annual rate of 1.4%. Assuming a Malthusian growth model, find the world population in 28 years.

An initial investment of $5000 earns 8.8% interest, compounded continuously. What will the investment be worth in 12 years? Please round the answer to the nearest cent. $__________

Write the logarithm as a sum and/or difference of logarithms of a single quantity. Then simplify if possible. Assume that w , r , t and a are positive numbers, and $a \neq 1$ . $\log _ { a } \frac { \sqrt [ 5 ] { w } } { \sqrt [ 3 ] { r t } }$

Let $f ( x ) = 5 x - 4$ and $g ( x ) = x ^ { 2 } + x$ . Find the composition. $( g \circ f ) ( x )$

Write the logarithmic expression as one logarithm. Assume that w is a positive number. $\log _ { 2 } w + \log _ { 2 } ( w + 2 ) - \log _ { 2 } 7$

Assume that $\log _ { b } 4 = 0.6021$ , $\log _ { b } 7 = 0.8451$ and $\log _ { b } 9 = 0.9542$ . Use these values to evaluate the logarithm. $\log _ { b } \frac { 9 } { 28 } =$ __________

Solve: $\log _ { 6 } x + \log _ { 6 } ( x - 20 ) = \log _ { 6 } 189$

The __________ function $g \circ h$ is defined by $( g \circ h ) ( x ) =$ __________.

Graph $f ( x ) = e ^ { x }$ .

Use the properties of logarithms to write the expression $\log _ { 4 } \frac { 4 x ^ { 9 } } { y }$ as a sum, difference, or multiple of logarithms. Assume x and y are positive numbers. Simplify if possible.

The illustration shows the graph of $f ( x ) = \ln x$ as well as a vertical translation of that graph. Using the notation $g ( x )$ for the translation, write the defining equation for the function. Assume that the translation is shifted by a whole number of units and the marks are one unit apart.