Solve 3^(2x-1)=3^(x=2)

Question

Please solve. 

Answer 1

Since both sides of the equation are three raised to some power, you can omit the base from the equation entirely.

So,

3^(2x-1) = 3^(x+2)

becomes

2x - 1 = x + 2

This is because in order for the two sides to be equal, the exponents on both sides have to be equal as well.

2x - x -1 + 1 = x - x + 2 +1

x = 3

Now checking back on your original equation

3^(2*3-1) = 3⁽³⁺²⁾

3⁵ = 3⁵