Math geniuses HELP??? LOGS?

Question

A house is expected to increase in value at an average rate of 7.5% p.a. How long will it take for 160000 house to be worth 250000?

EXPLANATIONS&ANSWERS PLEASE!!!!!!!!

THXXXXXXXXXX SO MUCH ;] I HATE LOGS OMG

Answer 1

log of 1.075 is 0.0314

log of 250000/160000 is 0.1938

0.1938/0.0314 = 6.17

to the nearest year, it is 6 years. if you want a more precise answer, break it into smaller time periods:

the log of 1.075, divided by 12 (I used calculator without rounding here until after dividing by 12) is 0.002617. This is the log of the percentage gain every MONTH.

so then 0.1938/0.002617 = 74.05 months. So to the nearest month, 74 months.

and so on.

just remember that for like terms, when multiplied, exponents add.

same as x^2 times x^2 = x^4, x^0.17 times x^0.33 = x^0.50, which could be expressed in a sentence as "the hundreth root of a number, to the power of 17, times the hundreth root of a number, to the power of 33, equals the hundreth root of that number, to the power of 50, which in turn equals the square root of that number, since the number is the hundreth root of itself, to the power of 100"

it is nothing more than a big chain of multiplication of roots, that's all log is about.