# Math Help - logarithm help required...

1. ## logarithm help required...

hello there everyone.

how would to go around solving a question such as this....

if an object doubles in size every 15 months, how long would it take to reach 10 times its original size, given the rate of expansion remains constant.

any help is appreciated.

2. Originally Posted by Paulotron
hello there everyone.

how would to go around solving a question such as this....

if an object doubles in size every 15 months, how long would it take to reach 10 times its original size, given the rate of expansion remains constant.

any help is appreciated.
If an object doubles in size every 15 minths its size after t months is:

$
S=S_0 2^{t/15}
$
.

So time for size to increase by a factor of 10 is the solution of:

$10=2^{t/15}$.

Take logs:

$\log(10)=\frac{t}{15}\log(2)$,

so:

$t=\frac{15 \log(10)}{\log(2)}$

RonL

3. fantastic thanks