SOLUTION: Solve: log base 5 (3x-1) - log base 5 (x+5)= 0

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Solve: log base 5 (3x-1) - log base 5 (x+5)= 0      Log On


   



Question 687515: Solve: log base 5 (3x-1) - log base 5 (x+5)= 0
Answer by MRperkins(300) About Me  (Show Source):
You can put this solution on YOUR website!
using the subtraction property of logarithms, we can combine the two logarithms and get log base 5 [(3x-1)/(x+5)]=0
Then, we can rewrite the problem in exponential form.
I always say "a to the b equals c" for a general exponential form and then drop the a down to the base, move the "b" to the right side of the equals sign, and then move the c to the left. It looks something like this:
Exponential form: a%5Eb=c
Logarithm form: log base a of c=b
So, in this case, our "a" is 5, our "b" is 0 and our "c" is %283x-1%29%2F%28x%2B5%29
and we can write it in exponential form:
5%5E0=%283x-1%29%2F%28x%2B5%29
well, 5%5E0=1 because of the zero exponent property and therefore 1=%283x-1%29%2F%28x%2B5%29
Multiply both sides by (x+5) and then solve for x
You can find my contact information at: http://www.scribblar.com/mg9yqg9 if you need additional help.