Question

Solve for x, where x is a real number
27^(2x)=9^(x-3)

could any1 please explain how to solve this step by step. I really want to be able to understand this. I already know x=-3/2

Answer 1

start with the fact that \(27=3^3\) and \(9=3^2\) to write both sides as of the equation with the same base of \(3\)

Answer 2

since \(27=3^3\) you can write
\[\large 27^{2x}=(3^3)^{2x}=3^{6x}\]

Answer 3

the right hand side becomes
\[\large 9^{x-3}=(3^2)^{x-3}=3^{2x-6}\]

Answer 4

now that the bases are the same set the exponents equal and solve
\[6x=2x-6\] for \(x\)

Answer 5

@satellite73 thank you! :)