Find x logarithms helpp

4(3^2x)=e^x

Details about calculation will welcome

thanks in advance

ln4 + 2xln3 = x
x - 2xln3 = ln4
x = ln4/(1 - 2ln3)

4(3^2x)=e^x; the question

=> ln 4 + 2 * x * ln 3 = x; take natural logarithm of both sides to get rid of exponential
=> ln 4 = x - 2*x * ln 3; subtract 2*x*ln 3 from both sides
=> x - 2*x * ln 3 = ln 4; reverse LHS, RHS to bring x to Left Hand Side
=> x * ( 1 - 2 * ln 3) = ln 4; take x outside as common factor
=> x = ln 4 / (1 - 2 ln 3); divide both sides with (1 - 2 ln 3)

I hope you have a scientific calculator. If not, search online for "scientific calculator" to get the answer, not given explicitly here to encourage you to think and do something for yourself.

4(3^2x) = e^x
log[ 4(3^2x) = log(e^x)
log 4 + log3^2x = loge^x
log4 + 2x log3 = x ans