Explanation:
3^x = 3 × 2^x
3^(x-1) = 2^x
now, let's apply the log of the base 2 to this.
log2(3^(x-1)) = x
logarithms of a specific base can be converted to logarithms of another base.
log b x = (log a x) / (log a b)
because I want to use log of the base 3 on the left hand side.
so,
log2(3^(x-1)) = log3(3^(x-1)) / log3(2) = (x-1)/log3(2)
(x-1)/log3(2) = x
x - 1 = x × log3(2)
x = x × log3(2) + 1
x(1 - log3(2)) = 1
x = 1/(1 - log3(2)) = 2.709511291...