help with log question

**ringo** · January 18th 2010, 02:30 PM

I've tried this problem several times and I always end up stuck, I would appreciate any help with it
(1/49) ^ (1+log7(2)) + 5 ^ –(log 1/5(7))

**Jhevon** · January 18th 2010, 02:46 PM

Originally Posted by ringo

I've tried this problem several times and I always end up stuck, I would appreciate any help with it
(1/49) ^ (1+log7(2)) + 5 ^ –(log 1/5(7))

do you mean $\displaystyle \left( \frac 1{49}\right)^{1 + \log_7 2} + 5^{- \log_{1/5} 7}$ ? And what do you want to do? simplify?

The identity you want to use here is: $a^{\log_a x} = x$

**ringo** · January 18th 2010, 02:54 PM

Originally Posted by Jhevon

do you mean $\displaystyle \left( \frac 1{49}\right)^{1 + \log_7 2} + 5^{- \log_{1/5} 7}$ ? And what do you want to do? simplify?

The identity you want to use here is: $a^{\log_a x} = x$

yes, that's what I meant, and I'm supposed to "evaluate".

**Jhevon** · January 18th 2010, 02:57 PM

Originally Posted by ringo

yes, that's what I meant, and I'm supposed to "evaluate".

Note that what you have is $(7^{-2})^{1 + \log_7 2} + \left( \frac 15 \right)^{\log_{1/5} 7}$

Now apply the rule i gave you (you have to tweak things a bit more).

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