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 /...
See This Answer Now
Start your subscription to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.
Already a member? Log in here.
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.