Question 1177564
26000 * 1.035 ^ n = 41000.
n is the number of years.


divide both sides of this equation by 26000 to get:


1.035 ^ n = 41/26


take the log of both sides of this equation to get:


log(1.035^n) = log(41/26).


by one of the log laws, this is equivalent to:


n * log(1.035) = log(41/26)


divide both sides of the equation by log(1.035) and solve for n to get:


n = log(41/26) / log(1.035) = 13.24001857.


confirm by replacing n in the original equation and solving to get:


f = 26000 * 1.035 ^ 13.24001857 = 41000.


13.24001857 years is your answer.


here's a reference on laws of logs.


<a href = "https://proofwiki.org/wiki/Laws_of_Logarithms" target = <"_blank">https://proofwiki.org/wiki/Laws_of_Logarithms</a>