Exam 5: Exponential and Logarithmic Functions and Equations

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $\frac { 1 } { 3 } ( \log 9 x + \log 9 y ) - 4 \log 9 ( x + 3 )$

Evaluate the logarithm without the use of a calculator. - $\log _ { 9 } \frac { 1 } { 729 }$

Solve the equation. - $\log _ { 4 } ( x - 3 ) = 3$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( y z ^ { 5 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 }$ (25x)

Write the exponential equation as an equation involving a logarithm. - $7 ^ { 3 } = 343$

Approximate the value using a calculator. Round your answer to three decimal places. - $\mathrm { e } ^ { 3.3 }$

Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. - $8 \ln x - \frac { 1 } { 3 } \ln y$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 4 } \frac { x ^ { 3 } } { y ^ { 6 } }$

Determine the correct exponential function of the form f(x) = b^x whose graph is given. -

Solve the problem. -The half-life of plutonium-234 is 9 hours. If 80 milligrams is present now, how much will be present in 6 days? (Round your answer to three decimal places.)

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \frac { 125 } { \sqrt { x - 1 } }$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ {\sqrt { 2 }} 224.9$

Use the change of base formula and a calculator to evaluate the logarithm. Round your answer to two decimal places. - $\log _ { 8 .5 }174$

Graph the function. -

Solve the problem. -Four bacteria are placed in a petri dish. The population will triple every day. The formula for the number of bacteria in the dish on day t $N ( t ) = 4 ( 3 ) ^ { t }$ , where t is the number of days after the four bacteria are placed in the dish. How many bacteria are in the dish six days after the four bacteria are placed in the dish?

Graph the function. -

Use transformations to graph the function. Determine the domain, range, and horizontal asymptote of the function. - $f ( x ) = - 2 ^ { x + 3 } + 4$

Find the domain of the function. - $f ( x ) = \ln ( - 4 - x )$

Solve the problem. -Suppose that you have $12,000 to invest. Which investment yields the greater return over 7 years: 8.75% compounded continuously or 8.9% compounded semiannually?