The given equation is
2^x+1 = 3^x
The first step is to take the log of both sides of the equation. We have
log 2^x+1 = log 3^x
We would apply one of the rules of logarithms which is expressed as
log (m^k) = klog m
By applying this rule to both sides of the equation, we have
(x + 1)log 2 = xlog 3
From the information given,
log 2 = A and log 3 = B
Substituting these values into the equation, we have
(x + 1)A = Bx
By expanding the parentheses on the left, we have
Ax + A = Bx
By collecting like terms, we have
Ax - Bx = - A
By factoring x on the left, we have
x(A - B) = - A
Dividing both sides of the equation by A - B,
x = - A/(A - B)