Rate of return with logs [engineering economics]

[Jim01]

Homework Statement

In 1903, a Picasso painting was purchased for $600. The family of the original owner sold the painting in 1995 for $29,152,000. What rate of return (interest) did the family receive on the investment?

Homework Equations

Single Payment Compound Interest Formula:

F = P(1+i)ⁿ

where,

F= a future some of money (future value)
P= a present sum of money
n= number of interest periods
i = interest rate per interest period.

The Attempt at a Solution

solve for i:

F = P(1+i)ⁿ
F/P = (1+i)ⁿ
log(F/P) = n log (1+i)

This is as far as I get. I know that n log (1+i) does not equal n log 1 + n log i, but I don't know what to do to isolate the i. I can't just divide both sides by n log because there is no such thing as n log. I thought about moving n log (1+i) to the left side and setting the equation to zero, but I didn't get anywhere with that either.

 

[danago]

Think about how you would invert a logarithmic function:

$$y = \log x \Leftrightarrow x = {10^y}$$

 

[xcvxcvvc]

get rid of the power of n by raising both sides by 1/n. i don't think that log trick you're pulling is even accurate