How do you solve 5 times 6^x = 6 times 5^x?
1 Answer
May 14, 2016
Explanation:
Given,
5*6^x=6*5^x
Take the logarithm of both sides since the bases are not the same.
log(5*6^x)=log(6*5^x)
Using the logarithmic property,
log(5)+log(6^x)=log(6)+log(5^x)
Group all terms with
log(6^x)-log(5^x)=log(6)-log(5)
Using the logarithmic property,
xlog(6)-xlog(5)=log(6)-log(5)
Factor out
x(log(6)-log(5))=log(6)-log(5)
Solve for
x=(log(6)-log(5))/(log(6)-log(5))
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