# How to simplify this log problem

• Sep 18th 2011, 09:59 AM
angypangy
How to simplify this log problem
I am asked to simply this formula:

d = ln(45)-ln(35) / ln(81) - ln(49)

Using the laws of logarithms I am supposed to simplify this expression and show that d = 1/2

I can see that d = ln(45/35)/ln(81/49) but not sure how that helps.

Can anyone give me a clue?
• Sep 18th 2011, 10:10 AM
e^(i*pi)
Re: How to simplify this log problem
Quote:

Originally Posted by angypangy
I am asked to simply this formula:

d = ln(45)-ln(35) / ln(81) - ln(49)

Using the laws of logarithms I am supposed to simplify this expression and show that d = 1/2

I can see that d = ln(45/35)/ln(81/49) but not sure how that helps.

Can anyone give me a clue?

Good start. Now a couple of hints for you:

$\dfrac{45}{35} = \dfrac{5 \times 9}{5 \times 7}$

and

$\dfrac{81}{49} = \left(\dfrac{9}{7}\right)^2$

Does that help?
• Sep 18th 2011, 12:26 PM
angypangy
Re: How to simplify this log problem
If it were 7/9 / 9^2/7^2 - then it cancels down to 7/9. But this is ln(7/9 / 9^2/7^2) - so can I do it the same way? Does it just become ln(7/9)?
• Sep 18th 2011, 12:33 PM
skeeter
Re: How to simplify this log problem
$\frac{\ln\left(\frac{9}{7}\right)}{\ln\left(\frac{ 9}{7}\right)^2} =$ ?