Question

Simplify `ln4+2ln4`?

Answer 1

`ln4+2ln4=ln64`

Explanation:

Remember two logarithmic identities,

1. `log_ax+log_ay=log_axy` and
2. `mlog_ax=log_ax^m`

Further `ln` is just `log` with base `e` and is better known as Napier's or natural log

Hence, `ln4+2ln4`

= `ln4+ln4^2`

= `ln(4xx4^2)`

= `ln64`

Answer 2

`ln64`

Explanation:

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

`•color(white)(x)logx+logy=log(xy)`

`•color(white)(x)logx^nhArrnlogx`

`rArrln4+2ln4`

`=ln4+ln4^2`

`=ln(4xx4^2)`

`=ln64`