Question

Write anwsers as fractions using / as fraction bar and write the greater value first

Answer 1

Final answer is
`(3)/(2)` or
`(1)/(2)`.

Explanation:

Given equation is
`\log_x\left(8x-3\right)-\log_x\left(4\right)=2`

Now we need to solve that equation for x.

`\log_x\left(8x-3\right)-\log_x\left(4\right)=2`

Apply formula
`\log_c\left(A\right)-\log_c\left(B\right)=\log_c\left((A)/(B)\right)`

`\log_x\left((8x-3)/(4)\right)=2`

Apply formula
`\log_c\left(A\right)=b \Rightarrow c^b=A`

`x^2=(8x-3)/(4)`

`4x^2=8x-3`

`4x^2-8x+3=0`

`4x^2-2x-6x+3=0`

`2x(2x-1)-3(2x-1)=0`

`(2x-3)(2x-1)=0`

`2x-3=0` or
`2x-1=0`

`2x=3` or
`2x=1`

`x=(3)/(2)` or
`x=(1)/(2)`

Hence final answer is
`(3)/(2)` or
`(1)/(2)`.