Question

How does 100=(4.7)^t become t=(ln(100))/(ln(4.7))

Answer 1

take the log of both sides
Recall that log(x^n) = n * logx

4.7^t = 100
log 4.7^t = log 100
t log 4.7 = log 100
t = log100/log4.7

Note that this is exactly the same as the one-step solution
t = log_{_4.7}100
but most calculators don't have a log_{_4.7} button