Convert Between Logarithmic and Exponent Form 2

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Question 1 of 5

1. Question
Convert into logarithmic form

$9 = 27^{\frac{2}{3}}$ $9=27^(2/3)$
- 1. $\log_{9} (\frac{2}{3}) = 27$ $log_9 (2/3)=27$
- 2. $\log_{27} (\frac{2}{3}) = 9$ $log_27 (2/3)=9$
- 3. $\log_{9} 27 = \frac{2}{3}$ $log_9 27=2/3$
- 4. $\log_{27} 9 = \frac{2}{3}$ $log_27 9=2/3$
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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

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

$\color{#00880a}{9}$ $=$ $=$ ${\color{#9a00c7}{27}}^{\frac{2}{3}}$

$N$ $N$ $=$ $=$ $9$ $9$

$a$ $a$ $=$ $=$ $27$ $27$

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

Substitute the components into the logarithmic form

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

$\log_{\color{#9a00c7}{27}} \color{#00880a}{9}$ $=$ $=$ $\frac{2}{3}$ $2/3$

$\log_{27} 9 = \frac{2}{3}$ $log_27 9=2/3$
Question 2 of 5

2. Question
Convert into exponent form

$\log_{2} 16 = 4$ $log_2 16=4$
- 1. $16 = 4^{2}$ $16=4^2$
- 2. $4 = 16^{2}$ $4=16^2$
- 3. $16 = 2^{4}$ $16=2^4$
- 4. $2 = 16^{4}$ $2=16^4$
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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 logarithmic form

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

$\log_{\color{#9a00c7}{2}} \color{#00880a}{16}$ $=$ $=$ $4$ $4$

$N$ $N$ $=$ $=$ $16$ $16$

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

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

Substitute the components into the exponent form

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

$\color{#00880a}{16}$ $=$ $=$ ${\color{#9a00c7}{2}}^4$

$16 = 2^{4}$ $16=2^4$
Question 3 of 5

3. Question
Convert into exponent form

$\log_{4} 8 = \frac{3}{2}$ $log_4 8=3/2$
- 1. $8 = 4^{\frac{3}{2}}$ $8=4^(3/2)$
- 2. $4 = 8^{\frac{3}{2}}$ $4=8^(3/2)$
- 3. $\frac{3}{2} = 4^{8}$ $3/2=4^8$
- 4. $\frac{3}{2} = 8^{4}$ $3/2=8^4$
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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 logarithmic form

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

$\log_{\color{#9a00c7}{4}} \color{#00880a}{8}$ $=$ $=$ $\frac{3}{2}$ $3/2$

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

$a$ $a$ $=$ $=$ $4$ $4$

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

Substitute the components into the exponent form

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

$\color{#00880a}{8}$ $=$ $=$ ${\color{#9a00c7}{4}}^{\frac{3}{2}}$

$8 = 4^{\frac{3}{2}}$ $8=4^(3/2)$
Question 4 of 5

4. Question
Convert into exponent form

$- \frac{3}{2} = \log_{2} (\frac{1}{2 \sqrt{2}})$ $-3/2=log_2 (1/(2sqrt2))$
- 1. $\frac{1}{2 \sqrt{2}} = 2^{- \frac{3}{2}}$ $1/(2sqrt2)=2^(-3/2)$
- 2. $\frac{1}{2 \sqrt{2}} = {(- \frac{3}{2})}^{2}$ $1/(2sqrt2)=(-3/2)^2$
- 3. $- \frac{3}{2} = {(\frac{1}{2 \sqrt{2}})}^{2}$ $-3/2=(1/(2sqrt2))^2$
- 4. $2 = {(\frac{1}{2 \sqrt{2}})}^{- \frac{3}{2}}$ $2=(1/(2sqrt2))^(-3/2)$
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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 logarithmic form

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

$\log_{\color{#9a00c7}{2}} \color{#00880a}{\frac{1}{2\sqrt{2}}}$ $=$ $=$ $- \frac{3}{2}$ $-3/2$

$N$ $N$ $=$ $=$ $\frac{1}{2 \sqrt{2}}$ $1/(2sqrt2)$

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

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

Substitute the components into the exponent form

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

$\color{#00880a}{\frac{1}{2\sqrt{2}}}$ $=$ $=$ ${\color{#9a00c7}{2}}^{-\frac{3}{2}}$

$\frac{1}{2 \sqrt{2}} = 2^{- \frac{3}{2}}$ $1/(2sqrt2)=2^(-3/2)$
Question 5 of 5

5. Question
Convert into exponent form

$\log_{2} 128 = 7$ $log_2 128=7$
- 1. $2 = 128^{7}$ $2=128^7$
- 2. $128 = 7^{2}$ $128=7^2$
- 3. $128 = 2^{7}$ $128=2^7$
- 4. $7 = 128^{2}$ $7=128^2$
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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 logarithmic form

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

$\log_{\color{#9a00c7}{2}} \color{#00880a}{128}$ $=$ $=$ $7$ $7$

$N$ $N$ $=$ $=$ $128$ $128$

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

$x$ $x$ $=$ $=$ $7$ $7$

Substitute the components into the exponent form

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

$\color{#00880a}{128}$ $=$ $=$ ${\color{#9a00c7}{2}}^7$

$128 = 2^{7}$ $128=2^7$

Convert Between Logarithmic and Exponent Form 2

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Quiz summary

Information

1. Question

Hint

Correct!

Exponent Form

Logarithmic Form

2. Question

Hint

Great Work!

Exponent Form

Logarithmic Form

3. Question

Hint

Well Done!

Exponent Form

Logarithmic Form

4. Question

Hint

Excellent!

Exponent Form

Logarithmic Form

5. Question

Hint

Keep Going!

Exponent Form

Logarithmic Form

Quizzes

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

$\color{#00880a}{9}$	$=$ $=$	${\color{#9a00c7}{27}}^{\frac{2}{3}}$

$N$ $N$	$=$ $=$	$9$ $9$
$a$ $a$	$=$ $=$	$27$ $27$

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

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

$\log_{\color{#9a00c7}{27}} \color{#00880a}{9}$	$=$ $=$	$\frac{2}{3}$ $2/3$

$N$ $N$	$=$ $=$	$16$ $16$
$a$ $a$	$=$ $=$	$2$ $2$
$x$ $x$	$=$ $=$	$4$ $4$

$N$ $N$	$=$ $=$	$8$ $8$
$a$ $a$	$=$ $=$	$4$ $4$

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

$N$ $N$	$=$ $=$	$\frac{1}{2 \sqrt{2}}$ $1/(2sqrt2)$

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

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

$N$ $N$	$=$ $=$	$128$ $128$
$a$ $a$	$=$ $=$	$2$ $2$
$x$ $x$	$=$ $=$	$7$ $7$