SOLUTION: Help! I need help with two problems on my pre-test for my finals. 1. Write log 125 base 5 = 3 in exponential form 2. Simplify:Log 6 base 6

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Help! I need help with two problems on my pre-test for my finals. 1. Write log 125 base 5 = 3 in exponential form 2. Simplify:Log 6 base 6       Log On


   

Question 112946: Help! I need help with two problems on my pre-test for my finals.
1. Write log 125 base 5 = 3 in exponential form
2. Simplify:Log 6 base 6

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Remember, any logarithm of the form log%28b%2C%28x%29%29=y can be written in exponential form as b%5Ey=x

#1
So log%285%2C125%29=3 can be written as 5%5E3=125

------------
#2
Now to simplify log%286%2C6%29, you can write the expression as log%286%2C6%29=y


Now rewrite the log as an exponent

log%286%2C6%29=y ====> 6%5Ey=6

So we can write the right side as 6%5E1 since anything to the first power is itself.


So we then get: 6%5Ey=6%5E1


Now since the bases are equal, the exponents are equal. In other words, y=1


So going back to log%286%2C6%29=y we can see that log%286%2C6%29=1