Exam 14: Exponential and Logarithmic Functions

Express $\log b \left( x \sqrt[7]{\frac{x}{y}} \right)$ as the sum or difference of simpler logarithmic quantities. Assume that all variables represent positive real numbers.

Find the common logarithm. $\log 0.3$ Express the values for log x to the nearest tenth.

For positive numbers b, r, and s, where $b \neq 1$ , $\log _ { b } ( r + s ) = \log _ { b } r + \log _ { 3 } s$ .

Evaluate the expression log₂8.

The symbol $\ln e$ is usually written instead of $\log _ { e } x$ .

Solve the equation. $10 ^ { x } = 0.0001$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log x = - 4.1687$

Write 10 ⁴ = 10,000 in logarithmic form.

Given that log 2 5 = 2.3219 and log 2 7 = 2.8074, evaluate the expression $\log _ { 2 } \sqrt [ 3 ] { 5 }$ by using properties: For positive real numbers b , r and s , where b $\neq$ 1, and for any real number p , $\log b r s = \log b r + \log b s$ $\log b \frac { r } { s } = \log b r - \log b s$ $\log b r ^ { p } = p ( \log b r )$ Please give the answer to four decimal places.

Perform the following calculations and express answer to the nearest hundredth. $\frac { \log 11 } { 4 \log 1.23 }$

Use the formula $A = p \left( 1 + \frac { r } { n } \right) ^ { n t }$ to find the total amount of money accumulated at the end of the indicated time period for the following investments: $1,500 for 5 years at 4.5% compounded quarterly. The choices are rounded to the nearest cent.

Determine whether the graph represents a one-to-one function. Please enter yes or no .

Solve the equation. $8 ^ { 6 x } = 4 ^ { x + 1 }$

A function that is decreasing over its entire domain is a one-to-one function.

Solve the equation. $\log 9 x = \frac { 3 } { 2 }$

Use the formula $A = p e ^ { r t }$ to find the total amount of money accumulated at the end of the indicated time period by compounding continuously: $13,000 for 12 years at 9%. The choices are rounded to the nearest cent.

Approximate the following logarithm to three decimal places. $\log _ { 5 } 0.83$

Find f - -1 ( x ). $f ( x ) = \sqrt { 5 x } \text { for } x \geq 0$

Use a calculator to find each common logarithm. Express answer to four decimal places. $\log 3527.7$

Solve the equation. $2 ^ { x } = 8$