SOLUTION: 2(3)^x=5^(x-1) I dont understand how to find x , can someone please help me?

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Question 20635: 2(3)^x=5^(x-1) I dont understand how to find x , can someone please help me?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
2(3)^x=5^(x-1)
trust you know logarithms...take logs on both sides ...use the formulae..
log x*y = log x + log y
log x^n= n*log x
taking logs we get
log 2+ log 3^x=(x-1)*log 5
log2+x log 3=(x-1) log 5=x log 5 - log 5
x(log 5-log 3)=log 2+ log 5=log 2*5 = log 10 =1
x log(5/3)=1
x = 1/log(5/3)