지수함수와 로그함수 전체 문제

Use the Change-of-Base Formula

In the following exercises, rounding to three decimal places, approximate each logarithm.

${\log }_{5}97$

Use the Change-of-Base Formula

In the following exercises, rounding to three decimal places, approximate each logarithm.

${\log }_{\sqrt{3}}16$

Solve Logarithmic Equations Using the Properties of Logarithms

In the following exercises, solve for x.

$3{\log }_{5}x={\log }_{5}216$

Solve Logarithmic Equations Using the Properties of Logarithms

In the following exercises, solve for x.

${\log }_{2}x+{\log }_{2}(x-2)=3$

Solve Logarithmic Equations Using the Properties of Logarithms

In the following exercises, solve for x.

$\log (x-1)-\log (3x+5)=-\log \,x$

Solve Logarithmic Equations Using the Properties of Logarithms

In the following exercises, solve for x.

${\log }_{4}(x-2)+{\log }_{4}(x+5)={\log }_{4}8$

Solve Logarithmic Equations Using the Properties of Logarithms

In the following exercises, solve for x.

$\ln (3x-2)=\ln (x+4)+\ln 2$

Solve Exponential Equations Using Logarithms

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

${2}^{x}=101$

Solve Exponential Equations Using Logarithms

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

${e}^{x}=23$

Solve Exponential Equations Using Logarithms

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

${\left(\frac{1}{3}\right)}^{x}=7$

Solve Exponential Equations Using Logarithms

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

$7{e}^{x+3}=28$

Solve Exponential Equations Using Logarithms

In the following exercises, solve each exponential equation. Find the exact answer and then approximate it to three decimal places.

${e}^{x-4}+8=23$

Jerome invests $\char36 18,000$ at age 17. He hopes the investments will be worth $\char36 30,000$ when he turns 26. If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Is that a reasonable expectation?

Elise invests $\char36 4500$ in an account that compounds interest monthly and earns $6\%.$ How long will it take for her money to double?

Researchers recorded that a certain bacteria population grew from 100 to 300 in 8 hours. At this rate of growth, how many bacteria will there be in 24 hours?

Mouse populations can double in 8 months $(A=2{A}_{0}).$ How long will it take for a mouse population to triple?

The half-life of radioactive iodine is 60 days. How much of a 50 mg sample will be left in 40 days?

For the functions, $f(x)=6x+1$ and $g(x)=8x-3,$ find ⓐ $(f\circ g)(x),$ ⓑ $(g\circ f)(x),$ and ⓒ $(f\cdot g)(x).$

Determine if the following set of ordered pairs represents a function and if so, is the function one-to-one. $\{(-2,2),(-1,-3),(0,1),(1,-2),(2,-3)\}$

Determine whether each graph is the graph of a function and if so, is it one-to-one.

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