solve the equation 3^(x-1)=24

Generally speaking, if the variable is in the exponent, use logs (either common logs or natural logs):

3^{x - 1}  =  24

Take the log of both sides:

log(3^{x - 1})  =  log(24)

The reason that logs are used is that the exponent within a logarithm comes out as a multiplier:

(x - 1)log(3)  =  log(24)

Now, divide both sides by the log(3):

x - 1  =  log(24) / log(3)                        If you want, simplify this by using a calculator ...

And, add 1 to both sides:

x  =  log(24) / log(3) + 1                       If you haven't used a calculator yet, use one now ...