SOLUTION: Solve for x, {{{ 12 = 2log(5,3^x) }}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve for x, {{{ 12 = 2log(5,3^x) }}}      Log On


   

Question 1189403: Solve for x,
+12+=+2log%285%2C3%5Ex%29+
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
12=2xlog 5 (3); 6=x log 5 (3)
leave the 6 alone for now and then change the base for the other side:
change of base log 5(3)=log 10 (3)/log 10 (5)=0.6826
6=0.6826 x
x=8.7898
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Also 6=log (5)3^x
raise everything to the 5th power
15625=3^x
logs of both sides
4.1938=x log 3
divide by log 3.