How many solutions does the equation`(8^x + 27^x)/(12^x +18^x)` = `7/6`have? (A) Exactly one (B) Exactly two (C) Finitely many (D) Infinitely many

Explanation

Let `2^x=a` and `3^x=b`

so equation becomes

`(a^3 + b^3)/(a^2b +b^2a)` = `7/6`

`(a^2 + b^2-ab)/(ab)` = `7/6`

=`6a^2-13ab+6b^2`

=`(2a-3b)(3a-2b)=0`

so,`2^(x+1)=3^(x+1)`

or `2^(x-1)=3^(x-1)`

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