I dont know how to simplify this logarithm

**burdonjo** · October 21st 2009, 10:43 AM

I am unsure how to simplify this expression, would someone be able to help me out pleeeaasssseee

2^(log8 7)

it is log base 8, i just was unsure how to change the font size

thank you

**earboth** · October 21st 2009, 12:13 PM

Originally Posted by burdonjo

I am unsure how to simplify this expression, would someone be able to help me out pleeeaasssseee

2^(log8 7)

it is log base 8, i just was unsure how to change the font size

thank you

Maybe you know that $8^{\frac13} = 2$

$2^{\log_8 7} = \left(8^{\frac13} \right)^{\log_8 7} = \left(8^{\log_8 7} \right)^{\frac13} = 7^{\frac13} = \sqrt[3]{7}$

**Soroban** · October 21st 2009, 12:22 PM

Hello,l burdonjo!

There are a number of approaches.
Here's mine . . .

Simplify: . $2^{\log_87}$

We have: . $2^{\log_87} \;=\;\left(8^{\frac{1}{3}}\right)^{\log_87} \;=\;(8)^{\frac{1}{3}\log_87} \;=\;(8)^{\log_8\left(7^{\frac{1}{3}}\right)}\;=\; 7^{\frac{1}{3}} \;=\;\sqrt[3]{7}$

Edit: Too fast for me, E.B.
.

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