Algebraically find the intersection 12=5^x Please show work. Thanks?

12 = 5^x
take the log of both sides
log 12 = log (5^x)
log 12 = x(log 5)
x = log 12/log 5 = 1.544

5^x = 12
x = (ln(12) + 2*i*pi*n) / ln(5), for any integer n
x =~ 1.543959310632771396474779496799 + 3.9039625316623427965473047644973*i*n, for any integer n
If x is a real number, then n = 0, so x = log[5](12) =~ 1.543959310632771396474779496799

a^x = b ---> x = ln(b)/ln(a)

log(base5)of 12 = x