Exam 4: Exponential and Logarithmic Functions

Solve the problem. -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 $\mathrm { pH }$ of a solution is given by $\mathrm { pH } = - \log x$ where $x$ represents the concentration of the hydrogen ions in the solution in moles per liter. Find the $\mathrm { pH }$ if the hydrogen ion concentration is $2.8 \times 10 ^ { - 3 }$ .

Evaluate or simplify the expression without using a calculator. - $\ln 1$

Graph the function. -Use the graph of $f ( x ) = \log x$ to obtain the graph of $g ( x ) = \log ( x - 1 )$ .

The graph of a logarithmic function is given. Select the function for the graph from the options. -28

Graph the function by making a table of coordinates - $f(x)=\left(\frac{1}{3}\right)^{x}$

Evaluate the expression without using a calculator. - $\log _ { 11 } 11$

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

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

Evaluate the expression without using a calculator. - $\log _ { 12 } \sqrt { 12 }$

Find the domain of the logarithmic function. - $f ( x ) = \log _ { 4 } ( x - 2 )$

Graph the function. -Use the graph of $\log _ { 5 } x$ to obtain the graph of $f ( x ) = 2 \log _ { 5 } x$ .

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log ( 100 x )$

Evaluate the expression without using a calculator. - $\ln \frac { 1 } { e ^ { 7 } }$

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 5 } \sqrt { 3 x }$

Graph the function. -Use the graph of $f ( x ) = \ln x$ to obtain the graph of $g ( x ) = - 3 \ln x$ .

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

Approximate the number using a calculator. Round your answer to three decimal places. - $2 ^ { 1.7 }$

Solve the problem. -The $\mathrm { pH }$ 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 The $\mathrm { pH }$ of a solution is given by $\mathrm { pH } = - \log x$ where $x$ represents the concentration of the hydrogen ions in th solution in moles per liter. Find the $\mathrm { pH }$ if the hydrogen ion concentration is $1 \times 10 ^ { - 2 }$ .

Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. - $\log _ { 7 } \left( \frac { 7 } { x } \right)$

Evaluate the expression without using a calculator. - $\log _ { 10 } 10,000$