SOLUTION: a certain investment fund multiplies the value of an investment by 4 every year. Thus, after n years, the value of the investment is multiplied by 4^n. how many years will it take

Question 157424: a certain investment fund multiplies the value of an investment by 4 every year. Thus, after n years, the value of the investment is multiplied by 4^n. how many years will it take for the value of the investment to be multiplied by 256?
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
n = 4
4^4 = 256.
n = 1, multiply by 4
n = 2 multiply by 4 again = 16
n = 3 multiply by 4 again = 64
n = 4 multiply by 4 again = 256
solved by using logarithms although n was so small it could have been done by simply working up each year as shown above.
n = log of 256 to the base 4 is the same as n = log of 256 to the base 10 divided by log of 4 to the base 10.
this allows the calculator to be used.
log of 256 to the base 10 = 2.408........
log of 4 to the base 10 = .602..................
n = log of 256 to the base 10 / log of 4 to the base 10 = 4
n = 4
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