How do you solve logx8=3?

1 Answer
Dec 4, 2015

x=12

Explanation:

logx8=3
logx23=3
3logx2=3 (The logarithm of the 3rd power of a number is 3 times the logarithm of the number itself)
Divide both side into 13, in order to simplify left side:
133logx2=13(3)
logx2=1
x1=2 (definition of logarithm)
Multiply both side by x:
xx1=x2
2x=x0 (If we take the product of two exponentials with the same nonzero base, we simply add the exponents)
Multiply both side by 12, in order to simplify left side:
122x=121
x=12