Question

Find n such that 1.005^n = 3

Answer 1

\[n=\frac{\ln(3)}{\ln(1.005)}\] by the change 'o base formula

Answer 2

\[b^x=y\iff x=\frac{\ln(y)}{\ln(b)}\]

Answer 3

I was working in that direction, but I wasn't sure about the log operation. The way I was doing it was nln(1.005) = ln(3), and of course divide the ln's to get n. Is that right? The exponent comes down to the front of the log in that case?

Answer 4

...in all cases?