Ok so how do you solve the following equation?

#9^x=3^(x-1)#

Thanks!

1 Answer
Jim G.
Feb 7, 2017

#x=-1#

Explanation:

#"left side "=9^x=(3^2)^x=3^(2x)#

#rArr3^(2x)=3^(x-1)larr" equation to be solved"#

Since the bases are equal. That is both 3, then we can equate the exponents.

#rArr2x=x-1rArrx=-1#

#color(blue)"As a check"#

Substitute this value into the equation and if the left side is equal to the right side then it is the solution.

#"left side "=9^-1=1/9#

#"right side "=3^-2=1/3^2=1/9#

#rArrx=-1" is the solution"#

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