Question

If logx(8x-3) -logx^4=2 the value of x is

Answer 1

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

Explanation:

`log_(x) (8x - 3)-log_(x) (4)=2`

We can simplify this by using the rules of logarithms to
`(log_(x)(8x-3) )/(log_(x)(4) ) =2`

By using another rule of logarithms we can rewrite the equation as
`(8x-3)/(4) =x^(2)`

Then we can multiply both sides by 4 to get rid of the fraction on the left side: 8x - 3 = 4x²

Then we can move all the terms to one side so we can have a polynomial to factor out and solve for x: 4x² - 8x + 3 = 0

Factoring this we get (2x - 1)(2x - 3) = 0

Setting each individual part equal to zero we get
`x=(1)/(2),(3)/(2)`