SOLUTION: What is log base 10 cube root of 10? I keep getting Log10 1/3

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Question 943582: What is log base 10 cube root of 10?
I keep getting Log10 1/3
Found 3 solutions by josmiceli, MathTherapy, macston:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+log%28+root%28+3%2C+10+%29+%29+
+log%28+10%5E%281%2F3%29+%29+
+%28+1%2F3%29%2A+log%28+10+%29+
+%28+1%2F3%29%2A1+=+1%2F3+
--------------------
The rules you need are:
+log%28+a%5Eb+%29+=+b%2Alog%28a%29+
and
+log%28+a%2Ca+%29+=+1+

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!
What is log base 10 cube root of 10?
I keep getting Log10 1/3


highlight_green%281%2F3%29, derived as follows:

log+%2810%2C+root+%283%2C+10%29%29______highlight%28highlight%28log+%2810%2C+10%5E%281%2F3%29%29%29%29, which means: 10%5Ex+=+1%5E%281%2F3%29, and subsequently, x+=+1%2F3

Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
The log is the exponent of the base that gives you a number For example log 100 is 2 because 2 is the exponent of 10 (the base) that gives us 100. The cube root of 10 is 10%5E%281%2F3%29 (The exponent is 1/3) so the log base 10 of the cube root of 10 is 1/3.