Isolating an exponent

Subject: isolating an exponent when it is a variable

Name: c. scott
Who is asking: Student
Level: Secondary

Question:
(math problem) Suppose you invest $500.00 in an account that pays 10% interest compounded annually. How long will it take for this value to triple?

A=p(1 + i)^a A=1500 i=0.1
1500=500(1.1)^a p=500 a=unknown

How do you solve this problem algebraicly? How do you isolate the variable (a) when it is an exponent?

Hi,

You are almost there. If

1500 = 500(1.1)^a

then divide both sides by 500 to get

3 = (1.1)^a

If you take a logarithm of both sides this becomes

log(3) = log((1.1)^a) = a log(1.1)

and hence

a = log(3)/log(1.1)

Cheers,
Harley Go to Math Central