Natural Logarithm approach!

Algebra Level 1

Solve:

e 2 ln ⁡ ( 5 ) \displaystyle \large e^{2 \ln (5) }


The answer is 25.

A Former Brilliant Member by A Former Brilliant Member

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5 solutions

Md Omur Faruque
Sep 4, 2015

e 2 ln ⁡ 5 = e ln ⁡ 5 2 = e ln ⁡ 25 = 25 e^{2\ln 5}=e^{\ln5^2}=e^{\ln25}=\color{#0C6AC7} {\boxed {25}} Or, x = e 2 ln ⁡ 5 x=e^{2\ln5} ⇒ ln ⁡ x = 2 ln ⁡ 5 = ln ⁡ 5 2 = ln ⁡ 25 \Rightarrow \ln x=2\ln 5=\ln5^2=\ln25 ⇒ x = 25 \Rightarrow x=\color{#0C6AC7} {\boxed {25}}

3 Helpful 0 Interesting 0 Brilliant 0 Confused

e 2 ln ⁡ ( 5 ) = e ln ⁡ 5 2 = 2 5 ln ⁡ e = 2 5 1 = 25 \large{e^{2 \ln (5)} =e^{\ln 5^2}=25^{\ln e}= 25^1=\boxed{25}}

Why ln ⁡ e = 1 \displaystyle \ln e=1 ?

ln ⁡ e = x \ln e=x e x = e e^x=e ln ⁡ e x = ln ⁡ e \ln e^x=\ln e ⇒ x ln ⁡ e = ln ⁡ e ⇒ x = 1 \Rightarrow x \ln e=\ln e \Rightarrow x=1

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Jingyang Tan
Sep 15, 2015

Use A Calculator and you will get the answer like ME!!!!

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Syed Baqir
Sep 4, 2015

100 points --------------lol

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Please, only post solutions in the solution section.

MD Omur Faruque - 5 years, 9 months ago

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Ok ,, Next time ...... Cheers :D

Syed Baqir - 5 years, 9 months ago
Arun Kumar
Sep 4, 2015

e^2ln5 =e^ln25=25^lne=25

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You mean e 2 ln ⁡ ( 5 ) = e ln ⁡ ( 25 ) = 2 5 ln ⁡ e = 25 e^{2 \ln (5)} = e^{\ln(25)} = 25^{\ln e} = 25 ?

A Former Brilliant Member - 5 years, 3 months ago

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