Question

Help with #3 i don’t know how to isolate x

Answer 1

Introduction

Hello, I'm Galaxy and I'll be helping you today.

You seem to have an issue with isolating
`x`, and solving for the equation. Here is how you'd go about.

Simplification

The first thing you want to do is to go ahead and simplify the equation, we know by our logarithm properties that when you subtract two logarithms with the same base, in this case
`√(3)`. An example of this property:
`\log _(10) a - \log _(10) b = \log _(10) (a)/(b)`

After using this property, we've simplified our equation down into:

`\log _(√(3)) (sin x)/(cos x) = \log _(√(3)) tan x = 0`

Notice how we have
`sin` over
`cos` in our equation, this translates over to

`tan`.

Finally, we can rewrite this as a simple equation:

`(√(3))^(0) = tan x\\tan x = 1`

Trigonometry

The next part to this is to solve using Trigonometry.

We can find the values where
`tan x` is equal to 1 and in our given range.

After that, we see that the solution is
`(\pi)/(4)` or 45°.

Cheers,

Galaxy