Question

Rewrite the logarithmic expression as a single logarithm and simplify the result.

Answer 1

\[\ln(\sin \theta^2)-\ln(\tan \theta^2)\]

Answer 2

\(\color{black}{\displaystyle \ln\left[(\sin \theta)^2\right]-\ln\left[(\tan \theta)^2\right]}\) ?

Answer 3

or, is it for some angle \(\theta^2\) ?

Answer 4

the first one

Answer 5

Another correct way to write the first one is:
\(\color{black}{\displaystyle \ln\left[\sin^2\theta\right]-\ln\left[\tan^2\theta\right]}\)

Answer 6

anyway ...

Answer 7

ok

Answer 8

The first rule you need is:
1. \(\color{black}{\displaystyle \ln\left[a^k\right]=k\times \ln[a]}\)

Answer 9

Apply this to \(\color{black}{\displaystyle \ln\left[(\sin \theta)^2\right]}\) and to \(\color{black}{\displaystyle \ln\left[(\tan \theta)^2\right]}\). Then write what you get.

Answer 10

(Don't be afraid to get anything wrong if you want to attempt.)

Answer 11

ok gimme a minute

Answer 12

2 ln |cos\[\theta\]