SOLUTION: In the equation: 0.8 = 5^n, how do you solve for n? So far I have this: nth root(8) = nth root(5^n) nth root(8) = 5 Where do I go from here?

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: In the equation: 0.8 = 5^n, how do you solve for n? So far I have this: nth root(8) = nth root(5^n) nth root(8) = 5 Where do I go from here?      Log On


   

Question 7173: In the equation: 0.8 = 5^n, how do you solve for n?
So far I have this:
nth root(8) = nth root(5^n)
nth root(8) = 5
Where do I go from here?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You should use logarithms on this problem.
0.8+=+5%5En Take the log of both sides:
log%280.8%29+=+nlog%285%29 Divide both sides by log(5)
n+=+log%280.8%29%2Flog%285%29 Do this in your calculator for more accuracy.
n+=+-.09691%2F.69897
n+=+-.13865 Approximately
Use your calculator to check:
5%5E-.13865+=+0.7999996