Solve 2^x=3

2^x  =  3

Whenever the unknown is in the exponent, use logarithms. You can use either log (common logs) or ln (natural logs).

Take the log of both sides:

log(2^x)  =  log (3)                       

A property of logarithms is that the exponent comes out as a multiplier:

x·log(2)  =  log(3)

x  =  log(3) / log(2)

x  ≈  1.585

I could have used  ln  instead of  log ; the steps and the answer would be the same.