Exam 9: Exponential and Logarithmic Functions

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 10 } 3 + \log _ { 10 } \left( x ^ { 3 } - 5 \right) + \log _ { 10 } 4$

Approximate the logarithm to four decimal places using the change of base formula. - $\log _ { 1 / 5 } 2$

Decide whether the statement is true or false. - $\log _ { 5 } 25 + \log _ { 5 } 125 = 5$

Solve the equation. Give an exact solution. - $\mathrm { e } ^ { ( \mathrm { x } + 8 ) } = 6$

Solve. Round the answer to the nearest whole. -An accidental spill of 80 grams of radioactive material in a local stream has led to the presence of radioactive debris decaying at a rate of $4 \%$ each day. Find how much debris still remains after 10 days.

Solve the equation. - $4 ^ { x } = 64$

Solve the equation for x. Give an approximate solution accurate to four decimal places. - $\log x = 1.7$

The reliability of a new model of CD player can be described by the exponential function R(t) = 2.7-(1/3)t, where the reliability R is the probability (as a decimal) that the CD player is still working t years after it is manufactured. Round the answer to the nearest hundredth. Then write your answer as a percent. -What is the probability that the CD player will still work $\frac { 1 } { 6 }$ of a year after it is manufactured?

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 2 } \frac { 7 \cdot 11 } { 13 }$

$f ( x ) = 3 x ^ { 3 } - 1 ; g ( x ) = 3 x ^ { 2 } - 1$ Find $( f \cdot g ) ( x )$

Write the expression as sums or differences of multiples of logarithms. - $\log _ { 7 } x ^ { 2 } ( x - 9 )$

For the given functions f and g, find the composition. - $f ( x ) = x ^ { 2 } + 9 x - 7 ; g ( x ) = \sqrt { x }$ Find $( f \circ g ) ( 9 )$ .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 2 } 12 + \log _ { 2 } 7$

For the given functions f and g, find the composition. - $f ( x ) = 6 x ^ { 2 } + 5 x ; g ( x ) = 2 x$ Find $( f \circ g ) ( x )$ .

Graph the function. - $y = \log _ { 1 / 3 } x$

Find the exact value. - $\log 0.0001$

Solve the equation. - $3125 ^ { x } = 25$

Fill in the blank with one of the words or phrases listed below. Some words or phrases may be used more than once. inverse common composition symmetric exponential vertical logarithmic natural half-life horizontal - $\mathrm { A } ( \mathrm { n } )$ ـــــــــــــــfunction is a function that can be defined by $f ( x ) = \log _ { b } x$ , where $x$ is a positive real number, $b$ is a constant positive real number, and $b$ is not 1 .

Express as the logarithm of a single expression. Assume that variables represent positive numbers. - $\log _ { 5 } ( x - 4 ) - \log _ { 5 } ( x + 6 )$

The graph of an exponential function is given. Match the graph to one of the following functions. -