Convert Between Logarithmic and Exponent Form 2

Quiz summary

0 of 5 questions completed

Questions:

–

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Lets see your results!

Points

Score

Time

Retry Quiz

Question 1 of 5

1. Question
Convert into logarithmic form

`9=27^(2/3)`
- `log_27 9=2/3`
- `log_9 27=2/3`
- `log_27 (2/3)=9`
- `log_9 (2/3)=27`
Hint

Help Video

Correct

Correct!

Incorrect

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` `=` `9`

`a` `=` `27`

`x` `=` `2/3`

Substitute the components into the logarithmic form

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

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

`log_27 9=2/3`
Question 2 of 5

2. Question
Convert into exponent form

`log_2 16=4`
- `16=2^4`
- `16=4^2`
- `4=16^2`
- `2=16^4`
Hint

Help Video

Correct

Great Work!

Incorrect

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`

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

`N` `=` `16`

`a` `=` `2`

`x` `=` `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`
Question 3 of 5

3. Question
Convert into exponent form

`log_4 8=3/2`
- `8=4^(3/2)`
- `4=8^(3/2)`
- `3/2=4^8`
- `3/2=8^4`
Hint

Help Video

Correct

Well Done!

Incorrect

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`

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

`N` `=` `8`

`a` `=` `4`

`x` `=` `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^(3/2)`
Question 4 of 5

4. Question
Convert into exponent form

`-3/2=log_2 (1/(2sqrt2))`
- `1/(2sqrt2)=2^(-3/2)`
- `1/(2sqrt2)=(-3/2)^2`
- `-3/2=(1/(2sqrt2))^2`
- `2=(1/(2sqrt2))^(-3/2)`
Hint

Help Video

Correct

Excellent!

Incorrect

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`

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

`N` `=` `1/(2sqrt2)`

`a` `=` `2`

`x` `=` `-3/2`

Substitute the components into the exponent form

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

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

`1/(2sqrt2)=2^(-3/2)`
Question 5 of 5

5. Question
Convert into exponent form

`log_2 128=7`
- `128=2^7`
- `128=7^2`
- `7=128^2`
- `2=128^7`
Hint

Help Video

Correct

Keep Going!

Incorrect

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`

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

`N` `=` `128`

`a` `=` `2`

`x` `=` `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`

Convert Between Logarithmic and Exponent Form 2

Try VividMath Premium to unlock full access

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

`N`	`=`	`128`
`a`	`=`	`2`
`x`	`=`	`7`