SOLUTION: Evaluate the expression without using a calculator: Log base 4 4^8 = ? I know the answer is 8 now but I'm not sure what the general rule is for solving this.

Question 1037867: Evaluate the expression without using a calculator:
Log base 4 4^8 = ?
I know the answer is 8 now but I'm not sure what the general rule is for solving this.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let log4(4^8) = y
by the basic definition of logarithms, log4(4^8) = y if and only if 4^y = 4^8.
4^y = 4^8 when y = 8.

you can also solve using your calculator as follows:

start with log4(4^8)
convert log of base 4 to the log of base 10 using the log base conversion formula.
you will get log4(4^8) = log10(4^8) / log10(4)
since log function of the calculator is the same as log10, then use your calculator to solve.
you get log10(4^8) / log10(4) = log(4^8)/log(4) which is equal to 8.

if you need a lesson on logs, then try this tutorial.
http://www.wtamu.edu/academic/anns/mps
/math/mathlab/col_algebra/index.htm
look at tutorials 42 through 47, paying special attention to 42 and 43 as they introduce the topic to you.
logs and exponents are related so it's good to know about exponential functions before looking at logs if you're not familiar with them.

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