exponents?

Question

can someone solve this by hand 50000=10000(1+.10/12)^12t

Answer 1

Is there suppose to be a decimal before 10/12? If yes,
50000/10000=(1+.10/12)^12t
5=(12.1/12)^12t
log5/log(12.1/12)=12t
t=(log5/log(12.1/12)/12
t=16.16
If no,
log5/log(11/6)/12=t
t=.22

Edit-Answer from Matt S is also correct. He used ln or natural log which is just another base. Both solutions give the same result as we have proved.

Answer 2

50000=10000 (1+.10/12)^12t

50000/10000=(1+.10/12)^12t

5=(1+.10/12)^12t

ln(5)=12t ln(1+.10/12)

t=ln(5)/(12*ln(1+.10/12)

t=ln(5)/(12*ln(12/12+.10/12)

t=ln(5)/(12*ln(12.1/12))

that's as far as you can do by hand then you'll need a calculator. Which yields the result

t=16.1613

Answer 3

Not very easily. You are asking how long does it take for an investment to increase 5x when it earns 10 percent yearly compounded monthly. Even a calculator approach would require trial-and-error.