# Thread: help with adding and subtracting logarithms

1. ## help with adding and subtracting logarithms

I'm having a hard time understanding why the following answer is 2

I know that log5(20) + log5(10) = log5(200) but I'm not sure how to deal with the -3log5(2) part...

I get the correct answer with my calculator but can this be solved without a calculator?

Thanks for the help

2. ## Re: help with adding and subtracting logarithms

Originally Posted by justincase13
I'm having a hard time understanding why the following answer is 2

I know that log5(20) + log5(10) = log5(200) but I'm not sure how to deal with the -3log5(2) part...

I get the correct answer with my calculator but can this be solved without a calculator?

Thanks for the help
Yes, it can be solved quite easily without a calculator. Let's do it step by step.

$log_5(20) + log_5(10) - 3log_5(2) = log_5(20) + log_5(10) - log_5(2^3) = log_5\left(\dfrac{20 * 10}{2^3}\right) =$

$log_5\left(\dfrac{200}{8}\right) = log_5(25) = log_5(5^2) = 2log_5(5) = 2 * 1 = 2.$

3. ## Re: help with adding and subtracting logarithms

Thank you so much