Question

How do you condense `ln 3 − 2 ln 5 + ln 10`?

Answer 1

`ln( 30/25)`

Explanation:

Adding logs means you were multiplying the numbers and dividing numbers means you were dividing the numbers.

`ln3 - 2ln5 + ln10 rArr ln3 - ln5^2 + ln10`

=`ln[(3xx10)/5^2]`

=`ln (30/25)`

Answer 2

`ln(6/5)`

Explanation:

Using the `color(blue)"laws of logarithms"`

`•lnx+lny=ln(xy)........ (1)`

`•lnx-lny=ln(x/y)........ (2)`

`•lnx^nhArrnlnx........ (3)`

These laws may be used on logarithms to any base.

Using (1) :`ln3+ln10=ln(3xx10)=ln30`

Using (3): `2ln5=ln5^2=ln25`

Using (2):`ln30-ln25=ln(30/25)=ln(6/5)`

`rArrln3-2ln5+ln10=ln(6/5)`