Convert from logarithmic form to exponential form Algebra II

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

2^{x}=8

x^{2}=8

8^{x}=2

x^{8}=2

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

b^{2}=100

100^{b}=10

b^{10}=100

10^{b}=100

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

m^{e}=e^{3}

e^{m}=e^{3}

e^{m}=3

m^{3}=e

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

2^{-t}=\dfrac{1}{16}

t^{\frac{1}{2}}=16

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

t^{\frac{1}{2}}=\dfrac{1}{16}

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

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

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

\left( \dfrac{1}{25}\right)^{u}=5

u^{2}=\dfrac{1}{25}

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

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

10^{p}=\dfrac{1}{2}

p^{10}=\sqrt{10}

10^{p}=\sqrt{10}

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

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

e^{k}=\dfrac{3}{4}

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

k^{\frac{3}{4}}=e