01 76 38 08 47
Kartable logo
HomeBrowseSearchLog in

To enjoy 10 free documents.

Kartable logo
HomeBrowseSearchLog in

To enjoy 10 free documents.

  1. Home
  2. 12th grade
  3. Algebra II
  4. Exercise : Convert from logarithmic form to exponential form

Convert from logarithmic form to exponential form Algebra II

Given \log_2\left(8\right)=x, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\log_2\left(8\right)=x

2^{x}=8

Given \log\left(100\right)=b, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\log\left(100\right)=b

10^{b}=100

Given \ln\left(e^{3}\right)=m, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\ln\left(e^{3}\right)=m

e^{m}=e^{3}

Given \log_\dfrac{1}{2}\left(16\right)=t, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\log_\dfrac{1}{2}\left(16\right)=t

\left( \dfrac{1}{2}\right)^{t}=16

Given \log_5\left(\dfrac{1}{25}\right)=u, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\log_5\left(\dfrac{1}{25}\right)=u

5^{u}=\dfrac{1}{25}

Given \log\left(\sqrt{10}\right)=p, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\log\left(\sqrt{10}\right)=p

10^{p}=\sqrt{10}

Given \ln\left(\sqrt[4]{e^{3}}\right)=k, convert the equation to exponential form.

In general:

\log_a\left(b\right)=c

if and only if:

a^{c}=b

In our problem:

\ln\left(\sqrt[4]{e^{3}}\right)=k

e^{k}=\sqrt[4]{e^{3}}

The editorial charter guarantees the compliance of the content with the official National Education curricula. Learn more

The courses and exercises are written by the Kartable editorial team, made up of teachers certified and accredited. Learn more

See also
  • Course : Exponential and logarithmic equations and inequalities
  • Exercise : Solve equations of the form a^x=b
  • Exercise : Solve equations of the form x^a=b
  • Exercise : Solve inequalities of the form a^x > or < b
  • support@kartable.com
  • Legal notice

© Kartable 2026