Question

Solve for x. 27^(2x)=9^(x-3) ...?

Answer 1

The answer is
`x = - (4)/(3)`


`27^(2x) = 9^((x-3)) \\ (3^(3) )^(2x) = (3^(2)) ^((x-3)) \\ \\ (x^(a) )^(b)= x^(a*b) \\  3^(3*2x) =3^(2*(x-3)) \\ 3^(6x) =3^((2x-6))`

Now, logarithm both sides of the equation:

`log(3^(6x) )=log(3^((2x-6))) \\ \\ log (x^(a)) =a*log(x) \\ 6x*log(3)=(2x-6)*log(3)`

Divide both sides of the equation by log(3):

`6x=2x-6 \\ 6x-2x = -6 \\ 4x = -3 \\ x = - (4)/(3)`