How do you solve # 5 times 6^x = 6 times 5^x#?
1 Answer
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))#
#color(green)(|bar(ul(color(white)(a/a)color(black)(x=1)color(white)(a/a)|)))#