Mastering Logarithms: Simplifying 1/4ln(x+2) + 1/3ln(x+3) for Homework

[cragar]

Homework Statement

1/4ln(x+2) + 1/3ln(x+3)

Homework Equations

The Attempt at a Solution

k so i know when we add log we can mulptily them an the number in front
of it is the power.
so would it be ln{(x+2)(x+3)} do we just multiply the numbers in front of the logs or do we add them

 

[Dick]

a*ln(b)=ln(b^a). So if you want to combine the two logs I would bring the factors outside into the log as powers before combining them.

 

[cragar]

ok i got ya

 

[Mark44]

Also, I would interpret 1/4ln(x+2) + 1/3ln(x+3) as you probably meant it (with the two ln terms in the numerators), but it might cause confusion with some people.

It's probably better to write this as 1/4 * ln(x+2) + 1/3 * ln(x+3), making it clearer that the first ln term is being multiplied by 1/4 and the second by 1/3.