6.7 Sample test

${\text{log}}_{3}3=$

${\text{log}}_{3}9=$

${\text{log}}_{3}27=$

${\text{log}}_{3}30=$

(approximately)

${\text{log}}_{3}1=$

${\text{log}}_3\left(\frac{1}{3}\right)=$

${\text{log}}_3\frac{1}{9}=$

${\text{log}}_3\left(-3\right)=$

${\text{log}}_{9}3=$

$3^{{\text{log}}_{3}8}=$

${\text{log}}_{-3}9=$

$\text{log}\mathrm{100,000}=$

$\text{log}\frac{1}{\text{100},\text{000}}=$

$\ln e^3=$

$\ln 4=$

Rewrite as a logarithm equation (no exponents): $q^z=p$

Rewrite as an exponent equation (no logs): ${\text{log}}_{w}g=j$

${\text{log}}_{5}240=$

${\text{log}}_5\left(\frac{3}{5}\right)=$

${\text{log}}_{5}1\frac{2}{3}=$

${\text{log}}_5{\left(\frac{3}{5}\right)}^2=$

${\text{log}}_{5}400=$

Graph $y=-{\text{log}}_{2}x+2$ .

What are the domain and range of the graph you drew in exercise #23?

I invest $200 in a bank that pays 4% interest, compounded annually. So after $y$ years, I have $200(1.04{)}^y$ dollars in the bank. When I come back, I find that my account is worth $1000. How many years has it been? Your answer will be a formula with a log in it .

The “loudness” of a sound is given by the formula $L=10\text{log}I$ , where $L$ is the loudness (measured in decibels), and $I$ is the intensity of the sound wave.

• A

  If the sound wave intensity is 10, what is the loudness?

• B

  If the sound wave intensity is 10,000, what is the loudness?

• C

  If the sound wave intensity is 10,000,000, what is the loudness?

• D

  What happens to the loudness every time the sound wave intensity multiplies by 1,000?

Solve for $x$ .

$\ln \left(3\right)+\ln \left(x\right)=\ln \left(21\right)$

Solve for $x$ .

${\text{log}}_2\left(x\right)+{\text{log}}_2(x+10)={\text{log}}_2\left(11\right)$