SOLUTION: Evaluate the logarithm please: {{{6^(log(6,5))}}} I think the correct answer is 5, based on the rule of logarithms and exponents, but not sure. Thanks.

Click here to see ALL problems on logarithm

Question 172996: Evaluate the logarithm please:

I think the correct answer is 5, based on the rule of logarithms and exponents, but not sure. Thanks.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Evaluate the logarithm please:

I think the correct answer is 5, based on the rule of logarithms and exponents, but not sure. Thanks.
------------
If it's 6 to the power of the log, then it is 5.
Your entry is that, but it doesn't display correctly.
It is 5.

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
6^(log6(5)) = 5
-------------------
You are correct.
In general b^(logb(a)) = a
Why?
b^(logb (a)) = x
Take the log of both sides to get:
log(x) = log[b^(logb (a)]
log(x) = (logb (a))*logb
log(x) = [log(a)/log(b)]
log(x) = log(a)
x = a
Therefore: x = b^[logb (a)] = a
=============================
Cheers,
Stan H.
=============================