Solve for x: 5^𝑥 = 3^𝑥-2

Question

Please help me with this question with a step by step

Answer 1

Please use parenthesis!!!

is it:

5^x = (3^x)-2

or

5^x = 3^(x-1)

??????

I will assume the latter, since the former

can only be solved numerically.

In fact there is not solution per Desmos website online tool.

Then

5^x = 3^(x - 2)

Takes log of both sides:

log (5^x) = log 3^(x-2)

Property of exponents:

x (log 5) = (x-2) (log 3)

Let A= log 5 and B = log 3

Then x*A = (x-2)B

Ax = Bx - 2B

Ax-Bx = -2B

x(A-b) = -2B

x = (-2b)/(A-b)

Leave the answer like that.