Solving using logs

Here's my question:

$541.39(1+i)¹⁵=784.09

Can you please show me how to do this?

grade 12

Rich Bolton

Hi Rich,

I expect that you want to find i. To isolate i on the left side of the equation you can divide both sides by 542.39 to get

(1 + i)¹⁵ = 784.09/542.39

Now take the log of both sides to get

log((1+i)¹⁵) = log(784.09/542.39)

The reason for using the logarithm here is that

log((1+i)¹⁵) = 15 log(1+i)

and hence the equation can be written

15 log(1+i) = log(784.09/542.39)

Can you complete the problem now?

Penny