# help with log question

• Jan 18th 2010, 02:30 PM
ringo
help with log question
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))
• Jan 18th 2010, 02:46 PM
Jhevon
Quote:

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

The identity you want to use here is: $\displaystyle a^{\log_a x} = x$
• Jan 18th 2010, 02:54 PM
ringo
Quote:

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

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

yes, that's what I meant, and I'm supposed to "evaluate".
• Jan 18th 2010, 02:57 PM
Jhevon
Quote:

Originally Posted by ringo
yes, that's what I meant, and I'm supposed to "evaluate".

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

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