SOLUTION: How do i solve log64^8=x The answer is 1/2 but how do you come about that answer? Also log5^1/5=x & log7^square root of 7=x These have me so confused.

Question 140699: How do i solve log64^8=x
The answer is 1/2 but how do you come about that answer?
Also log5^1/5=x & log7^square root of 7=x
These have me so confused.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming that the problem looks like this: ???

Start with the given equation

Rewrite the left side by using the change of base formula. Remember the change of base formula is

Rewrite 64 as

Rewrite the denominator using the identity

Divide and cancel like terms

Simplify

So the answer is

Start with the given equation

Rewrite the left side by using the change of base formula.

Rewrite 5 as . Notice how

Rewrite the denominator using the identity

Cancel like terms

Simplify

Reduce

So the answer is

Start with the given equation

Rewrite as

Rewrite the expression using the identity

Take the log base 7 of 7 to get 1. In other words,

Multiply

So the answer is

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