Solve the following logarithmic equation. Express irrational solutions in exact form. log8x=3

Answer 1

if you meant log of x to the base 8 = 3

then x=8^3 = 8x8x8 = 512

but if you meant log of 8x to the base `10 = 3

then 10^3 = 8x

x = (1000)/8 = 125

Answer 2

Here is an answer to the question making the assumption that the question was log₈(x)=3.

To solve an equation like this you have to be comfortable switching to exponential form. Remember a logarithm is an exponent! And 8 is the base. The number 3 is called the antilogarithm.

To convert to exponential form raise the base to the exponent (logarithm) and set equal to antilogarithm.

8³=x

x= 8(8)(8) = 512