SOLUTION: How do I solve for x in these two problems: logx1/64=-3 and logx5^3=3?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I solve for x in these two problems: logx1/64=-3 and logx5^3=3?      Log On


   

Question 231980: How do I solve for x in these two problems:
logx1/64=-3 and logx5^3=3?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
When the variable is the base of the logarithm, rewrite the equation in exponential form.

log%28x%2C+%281%2F64%29%29+=+-3
In exponential form this is:
x%5E%28-3%29+=+1%2F64
There are a variety of ways we can finish. One way would be to rewrite the left side with a positive exponent:
1%2Fx%5E3+=+1%2F64
And since 4%5E3+=+64, x must be 4.

log%28x%2C+%285%5E3%29%29+=+3
In exponential form this is:
x%5E3+=+5%5E3
I hope it is obvious the x=5.