Question

How do you simplify `ln 3 − 2 ln 8 + ln 16`?

Answer 1

`ln(3/4)`

Explanation:

We have to use the Logarithm Properties.

`ln(3)-2ln(8)+ln(16)`

We can rewrite the initial expression using the Power rule in this way
`ln(3)-ln(8^2)+ln(16)`

`ln(3)-ln(64)+ln(16)`

Here we use the Quotient rule
`ln(3/64)+ln(16)`

And here the Product rule
`ln(3/64*16)`

`ln(48/64)`

Finally we get the semplified version :
`ln(3/4)`

Answer 2

`ln(3/4)`

Explanation:

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

`•color(white)(x)logx^nhArrnlogx`

`•color(white)(x)logx+logyhArrlog(xy)`

`•color(white)(x)logx-logyhArrlog(x/y)`

`rArrln3-ln8^2+ln16`

`=ln((3xx16)/64)=ln(48/64)=ln(3/4)`