Convert Between Logarithmic and Exponent Form 1

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Question 1 of 4

1. Question
Convert into logarithmic form

$3^{4} = 81$ $3^4=81$
- 1. ${log}_{4} 3 = 81$ $log_4 3=81$
- 2. ${log}_{3} 4 = 81$ $log_3 4=81$
- 3. ${log}_{3} 81 = 4$ $log_3 81=4$
- 4. ${log}_{4} 81 = 3$ $log_4 81=3$
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Exponent Form

$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$

Logarithmic Form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$

First, identify the components of the equation that is given in exponent form

$\color{#00880a}{N}$ $=$ $=$ ${\color{#9a00c7}{a}}^x$

$\color{#00880a}{81}$ $=$ $=$ ${\color{#9a00c7}{3}}^4$

$N$ $N$ $=$ $=$ $81$ $81$

$a$ $a$ $=$ $=$ $3$ $3$

$x$ $x$ $=$ $=$ $4$ $4$

Substitute the components into the logarithmic form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$ $=$ $=$ $x$ $x$

$\log_{\color{#9a00c7}{3}} \color{#00880a}{81}$ $=$ $=$ $4$ $4$

${log}_{3} 81 = 4$ $log_3 81=4$
Question 2 of 4

2. Question
Convert into logarithmic form

$\frac{1}{2} = 2^{- 1}$ $1/2=2^(-1)$
- 1. ${log}_{- 1} 2 = \frac{1}{2}$ $log_(-1) 2=1/2$
- 2. ${log}_{2} 1 = - \frac{1}{2}$ $log_2 1=-1/2$
- 3. ${log}_{2} (- 1) = \frac{1}{2}$ $log_2 (-1)=1/2$
- 4. ${log}_{2} (\frac{1}{2}) = - 1$ $log_2 (1/2)=-1$
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Exponent Form

$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$

Logarithmic Form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$

First, identify the components of the equation that is given in exponent form

$\color{#00880a}{N}$ $=$ $=$ ${\color{#9a00c7}{a}}^x$

$\color{#00880a}{\frac{1}{2}}$ $=$ $=$ ${\color{#9a00c7}{2}}^{-1}$

$N$ $N$ $=$ $=$ $\frac{1}{2}$ $1/2$

$a$ $a$ $=$ $=$ $2$ $2$

$x$ $x$ $=$ $=$ $- 1$ $-1$

Substitute the components into the logarithmic form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$ $=$ $=$ $x$ $x$

$\log_{\color{#9a00c7}{2}} \color{#00880a}{\frac{1}{2}}$ $=$ $=$ $- 1$ $-1$

${log}_{2} (\frac{1}{2}) = - 1$ $log_2 (1/2)=-1$
Question 3 of 4

3. Question
Convert into logarithmic form

$25^{\frac{3}{2}} = 125$ $25^(3/2)=125$
- 1. ${log}_{25} 125 = \frac{3}{2}$ $log_25 125=3/2$
- 2. ${log}_{125} (\frac{3}{2}) = 25$ $log_125 (3/2)=25$
- 3. ${log}_{125} 25 = \frac{3}{2}$ $log_125 25=3/2$
- 4. ${log}_{25} (\frac{3}{2}) = 125$ $log_25 (3/2)=125$
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Exponent Form

$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$

Logarithmic Form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$

First, identify the components of the equation that is given in exponent form

$\color{#00880a}{N}$ $=$ $=$ ${\color{#9a00c7}{a}}^x$

$\color{#00880a}{125}$ $=$ $=$ ${\color{#9a00c7}{25}}^{\frac{3}{2}}$

$N$ $N$ $=$ $=$ $125$ $125$

$a$ $a$ $=$ $=$ $25$ $25$

$x$ $x$ $=$ $=$ $\frac{3}{2}$ $3/2$

Substitute the components into the logarithmic form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$ $=$ $=$ $x$ $x$

$\log_{\color{#9a00c7}{25}} \color{#00880a}{125}$ $=$ $=$ $\frac{3}{2}$ $3/2$

${log}_{25} 125 = \frac{3}{2}$ $log_25 125=3/2$
Question 4 of 4

4. Question
Convert into logarithmic form

$16^{\frac{3}{4}} = 8$ $16^(3/4)=8$
- 1. ${log}_{8} 16 = \frac{3}{4}$ $log_8 16=3/4$
- 2. ${log}_{16} 8 = \frac{3}{4}$ $log_16 8=3/4$
- 3. ${log}_{16} (\frac{3}{4}) = 8$ $log_16 (3/4)=8$
- 4. ${log}_{8} (\frac{3}{4}) = 16$ $log_8 (3/4)=16$
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Exponent Form

$\color{#00880a}{N}={\color{#9a00c7}{a}}^x$

Logarithmic Form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}=x$

First, identify the components of the equation that is given in exponent form

$\color{#00880a}{N}$ $=$ $=$ ${\color{#9a00c7}{a}}^x$

$\color{#00880a}{8}$ $=$ $=$ ${\color{#9a00c7}{16}}^{\frac{3}{4}}$

$N$ $N$ $=$ $=$ $8$ $8$

$a$ $a$ $=$ $=$ $16$ $16$

$x$ $x$ $=$ $=$ $\frac{3}{4}$ $3/4$

Substitute the components into the logarithmic form

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$ $=$ $=$ $x$ $x$

$\log_{\color{#9a00c7}{16}} \color{#00880a}{8}$ $=$ $=$ $\frac{3}{4}$ $3/4$

${log}_{16} 8 = \frac{3}{4}$ $log_16 8=3/4$

Convert Between Logarithmic and Exponent Form 1

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Quiz summary

Information

1. Question

Hint

Nice Job!

Exponent Form

Logarithmic Form

2. Question

Hint

Excellent!

Exponent Form

Logarithmic Form

3. Question

Hint

Fantastic!

Exponent Form

Logarithmic Form

4. Question

Hint

Keep Going!

Exponent Form

Logarithmic Form

Quizzes

$\color{#00880a}{N}$	$=$ $=$	${\color{#9a00c7}{a}}^x$
$\color{#00880a}{81}$	$=$ $=$	${\color{#9a00c7}{3}}^4$

$N$ $N$	$=$ $=$	$81$ $81$
$a$ $a$	$=$ $=$	$3$ $3$
$x$ $x$	$=$ $=$	$4$ $4$

$\log_{\color{#9a00c7}{a}} \color{#00880a}{N}$	$=$ $=$	$x$ $x$
$\log_{\color{#9a00c7}{3}} \color{#00880a}{81}$	$=$ $=$	$4$ $4$

$N$ $N$	$=$ $=$	$\frac{1}{2}$ $1/2$

$a$ $a$	$=$ $=$	$2$ $2$
$x$ $x$	$=$ $=$	$- 1$ $-1$

$N$ $N$	$=$ $=$	$125$ $125$
$a$ $a$	$=$ $=$	$25$ $25$

$x$ $x$	$=$ $=$	$\frac{3}{2}$ $3/2$

$N$ $N$	$=$ $=$	$8$ $8$
$a$ $a$	$=$ $=$	$16$ $16$

$x$ $x$	$=$ $=$	$\frac{3}{4}$ $3/4$