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.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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.      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the problem looks like this: log%2864%2C%288%29%29=x???


log%2864%2C%288%29%29=x Start with the given equation


log%2810%2C%288%29%29%2Flog%2810%2C%2864%29%29=x Rewrite the left side by using the change of base formula. Remember the change of base formula is log%28b%2C%28x%29%29=log%2810%2C%28x%29%29%2Flog%2810%2C%28b%29%29


log%2810%2C%288%29%29%2Flog%2810%2C%288%5E2%29%29=x Rewrite 64 as 8%5E2


log%2810%2C%288%29%29%2F%282%2Alog%2810%2C%288%29%29%29=x Rewrite the denominator using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


cross%28log%2810%2C%288%29%29%29%2F%282cross%28log%2810%2C%288%29%29%29%29=x Divide and cancel like terms


1%2F2=x Simplify


So the answer is x=1%2F2






log%285%2C%281%2F5%29%29=x Start with the given equation



log%2810%2C%281%2F5%29%29%2Flog%2810%2C%285%29%29=x Rewrite the left side by using the change of base formula.




log%2810%2C%281%2F5%29%29%2Flog%2810%2C%28%281%2F5%29%5E%28-1%29%29%29=x Rewrite 5 as %281%2F5%29%5E%28-1%29. Notice how 5=%281%2F5%29%5E%28-1%29


log%2810%2C%281%2F5%29%29%2F%28-1%2Alog%2810%2C%281%2F5%29%29%29=x Rewrite the denominator using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


cross%28log%2810%2C%281%2F5%29%29%29%2F%28-1%2Across%28log%2810%2C%281%2F5%29%29%29%29=x Cancel like terms


1%2F%28-1%29=x Simplify

x=-1 Reduce


So the answer is x=-1






log%287%2C%28sqrt%287%29%29%29=x Start with the given equation



log%287%2C%287%5E%281%2F2%29%29%29=x Rewrite sqrt%287%29 as 7%5E%281%2F2%29

%281%2F2%29%2Alog%287%2C%287%29%29=x Rewrite the expression using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


%281%2F2%29%2A1=x Take the log base 7 of 7 to get 1. In other words, log%287%2C%287%29%29=1


x=1%2F2 Multiply



So the answer is x=1%2F2