SOLUTION: this problem came from a teacher-made worksheet {{{3^(x-2) = 2 * 6^(2x)}}} ; {{{x=(log 2 + log 9)/(log 3 - log 36)= -1.163}}} I don't know where to start.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: this problem came from a teacher-made worksheet {{{3^(x-2) = 2 * 6^(2x)}}} ; {{{x=(log 2 + log 9)/(log 3 - log 36)= -1.163}}} I don't know where to start.      Log On


   

Question 133894: this problem came from a teacher-made worksheet
3%5E%28x-2%29+=+2+%2A+6%5E%282x%29 ; x=%28log+2+%2B+log+9%29%2F%28log+3+-+log+36%29=+-1.163
I don't know where to start.
Answer by Ganesha(13) About Me  (Show Source):
You can put this solution on YOUR website!
3^x-2 = 2.6^2x
Taking logarithms on both sides
(x-2)log3 = 2xlog2.6
xlog3 - 2log2.6 = 2log3
x(log3 - 2log2.6) = 2log3
x =2log3/(log3- 2log2.6) =log9/(log(3/2.6^2)) =-2.704573985
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The expression on the RHS 2.6^2x = 2*6^2x,then
the solution would be in the steps as above
x = (log2 + 2log3)/(log3 - 2log6) = log2*3^2/log3/360 =log 18/(-log12) =-1.63171163