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We have to solve for x given: 15^(2x-3)=3^x*5^(3x-6)

15^(2x-3)=3^x*5^(3x-6)

=> (5*3)^(2x - 3) = 3^x * 5^(3x - 6)

=> 5^(2x - 3) * 3^(2x - 3) = 3^x * 5^(2x - 3)* 5^x / 5^3

=> 3^(2x - 3) = 3^x * 5^x / 5^3

=> 125* 3^2x /...

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We have to solve for x given: 15^(2x-3)=3^x*5^(3x-6)

15^(2x-3)=3^x*5^(3x-6)

=> (5*3)^(2x - 3) = 3^x * 5^(3x - 6)

=> 5^(2x - 3) * 3^(2x - 3) = 3^x * 5^(2x - 3)* 5^x / 5^3

=> 3^(2x - 3) = 3^x * 5^x / 5^3

=> 125* 3^2x / 3^3 = 3^x * 5^x

=> 125 * 3^x * 3^x = 27 * 3^x * 5^x

=> 125 * 3^x = 27 * 5^x

=> 125 / 27 = 5^x / 3^x

=> (5/3)^3 = (5/3)^x

As the base is equal equate the exponent.

We get x = 3.

Approved by eNotes Editorial Team