How do you solve 9 to the power of x equals 243?

9x = 243

ln(9x) = ln(243)

xln(9) = ln(243)

x = ln(243)/ln(9)

x = 2.5

NB this works with log10 too.

NBB if you don't have a calculator, this kinda question will only have easy values of x like integer values or 0.5, so its always worth chucking numbers in.