solve for x and show all steps

Question

log_bx=2-a+log_b(a²b^a/b²⁾

Answer 1

Bring all log terms to the left side of the equation.

 

log_bx - log_b(a²b^a / b²) = 2 - a

 

 

Use the properties of logs on the left side.

 

log_b[xb² / a²b^a] = 2 - a

 

 

b^{(2 - a)} = xb² / a²b^a

 

b^{(2 - a)} = xb^{(2 - a)} / a²

 

 

Multiply both sides of the equation by   a² / b^{(2 - a)}.

 

a² = x

 

a = ±√x