Question 936601: simplify 0.056^2/3 using logarithms
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! not exactly sure why you would need logs to solve this.
you can simply put it in your calculator and get the answer.
the answer is that .056^(2/3) = .14637...
using logs to solve this is just a round about way to get to the same answer.
i'll do it just to show you.
start with:
y = .056^(2/3)
take the log of both sides of the equation to get:
log(y) = log(.056^(2/3))
since log(.056^(2/3)) = 2/3 * log(.056), your equation becomes:
log(y) = 2/3 * log(.056)
solve for log(y) to get:
log(y) = -.83454...
log(y) = -.83454... if and only if 10^-.83454... = y
use your calculator to find 10^-.83454... to get y = .14637...
you wind up with the same answer but you have to go round and round to get it.
there was no reason to use logs to solve this problem.
you would use logs if the unknown variable was in the exponent.
example:
8 = 2^x
take log of both sides to get log(8) = log(2^x) which becomes log(8) = x*log(2) which becomes x = log(8) / log(2) which becomes x = 3.
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