Exam 9: Inequalities and Problem Solving

Graph the function. - $\text { Use the graph of } f ( x ) = 3 ^ { x } \text { to obtain the graph of } g ( x ) = 3 ^ { x } - 2$

Graph the function. - $f(x)=\log _{2} x$

Evaluate the expression without using a calculator. -The long jump record, in feet, at a particular school can be modeled by f(x) = 18.8 + 2.2 ln(x + 1) where x is the number of years since the school was opened. What is the record for the long jump 25 years after the school Opened? Round the answer to the nearest tenth.

Evaluate the expression without using a calculator. - $\log 1000$

Evaluate the expression without using a calculator. -The pH of a solution ranges from 0 to 14. An acid has a pH less than 7. Pure water is neutral and has a pH of 7. The pH of a solution is given by pH = -log x where x represents the concentration of the hydrogen ions in the Solution in moles per liter. Find the pH if the hydrogen ion concentration is 5 × 10-12.

Find the domain of the logarithmic function. Write your answer in interval notation. - $f ( x ) = \log _ { 6 } ( x + 7 ) ^ { 2 }$

Evaluate the expression without using a calculator. - $\log 0.01$

The graph of an exponential function is given. Select the function for the graph from the functions listed. -

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\ln \left( \frac { \mathrm { e } ^ { 3 } } { 2 } \right)$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { b } \left( y z ^ { 8 } \right)$

Write the equation in its equivalent logarithmic form. - $2 ^ { 3 } = x$

Evaluate the expression without using a calculator. - $\ln \sqrt [ 8 ] { \mathrm { e } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 10 } ( 10,000 x )$

Evaluate the expression without using a calculator. - $\ln \mathrm { e } ^ { 4.3 }$

Write the equation in its equivalent logarithmic form. - $\sqrt [ 3 ] { 125 } = 5$

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. - $\log _ { 5 } 15 - \log _ { 5 } 3$

Use the compound interest formulas A $A = P \left( 1 + \frac { r } { n } \right) ^ { n t }$ and A = Pert to solve. -Suppose that you have $9000 to invest. Which investment yields the greater return over 7 years: 7.5% compounded continuously or 7.6% compounded semiannually?

Write the equation in its equivalent exponential form. - $3 = \log _ { b ^ { 2 } } 216$

Write the equation in its equivalent exponential form. - $\log _ { 4 } 256 = x$

Write the equation in its equivalent logarithmic form. - $8 ^ { x } = 359$