Nasty logarithm question?

Question

I have this problem on my math homework. Unfortunately, I put it off until the last minute and I don't remember how to do it.
We've been rewriting exponential functions and solving them. How do I do this?

100(1.04)^2t=300

And can you also explain the math behind what I'm doing for other problems.

Thank you!!

Answer 1

100(1.04)^2t = 300

divide both sides by the coefficient

(1.04)^2t = 3

Take the base 1.04 logarithm of both sides

2t = log_{1.04} 3

Divide by the coefficient, again

t = ½ log_{1.04} 3

t ≈ 14.005511(…)

Answer 2

100(log2(1.04)) / 300 = t

and i cant explain the other math cuz i dont see the problems haha but thats how you go about doin that.

Answer 3

Take log base 10 of both sides:

log(100) + 2t*log(1.04) = log(300)

2 + 2t*log(1.04) = 2+log(3)

2t*log(1.04) = log(3)

t = log(3) / 2*log(1.04)

t = 14.0