Write as a single logarithm 2ln(5)+ln(4)-3

Question

akashdeepdeb · Answer

ln means log to the base e
Now
2ln5 = ln 25
+ln4 - ln3
Now use log properties 

Ln A + Ln B = Ln (AB)
Ln A - Ln B = Ln (A/B)

So your question would equal

ln 25 * 4/3

Got it? :)

zepdrix · Answer

$$\Large 2\ln(5)+\ln(4)-3$$
I don't think the last term was supposed to be ln3.
Can you confirm that aem? D:

zepdrix · Answer

Is your problem this:$$\Large 2\ln(5)+\ln(4)-3$$This:$$\Large 2\ln(5)+\ln(4)-\ln(3)$$Or this:$$\Large 2\ln(5)+\ln(4-3)$$

aem9296 · Answer

this first one

zepdrix · Answer

Then we need to fix one thing :)

That last term isn't ln(3).

Instead what we'll do is some sneaky math to get a natural log attached to it.

zepdrix · Answer

Whenever the `insides` of our log match the `base` of our log, then it's equal to 1.

Examples:$$\Large \log_2(2)=1$$When no base is written it's a base of 10 right?$$\Large \log(10)=1$$

So we can also apply this to the natural log,$$\Large \color{royalblue}{\ln(e)=1}$$

zepdrix · Answer

$$\Large 2\ln(5)+\ln(4)-3\cdot\color{royalblue}{1}$$We want to be sneaky and multiply our 3 by 1.$$\Large 2\ln(5)+\ln(4)-3\cdot\color{royalblue}{\ln(e)}$$

zepdrix · Answer

Now all of our terms have logs so we can use rules of logarithms to write them as a single log! :D

Akash listed some nice steps above, we'd just need to deal with the 3 term a little differently.

aem9296 · Answer

OH okay! :) thanks so much!