Question

Which system of equation could be graphed to solve the equation below?

Answer 1

Option D.

Explanation:

The given equation is
`log_(0.5)x=log_(3)2+x`

As we know
`log_(0.5)x=(logx)/(log(0.5))`

and
`log_(2)3=(log3)/(log2)`

Now we replace these values in the given equation

`(logx)/(log(0.5))=(log3)/(log2)+x`

Therefore, option D will be the answer.

Answer 2

Using: loga b = log b / log a
1) a=x, b=0.5 → y1=log0.5 x → y1= log x / log 0.5
2) a=2, b=3 →y2=log3 2 +x → y2=log 2 / log 3 +x

Answer: Fourth option:
y1=log x / log 0.5 , y2= log 2 / log 3 +x