Question

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

Answer 1

Answer:

$x=\frac{1}{2},\frac{3}{2}$

Step-by-step explanation:

$log_{x} (8x - 3)-log_{x} (4)=2$

We can simplify this by using the rules of logarithms to $\frac{log_{x}(8x-3) }{log_{x}(4) } =2$

By using another rule of logarithms we can rewrite the equation as $\frac{8x-3}{4} =x^{2}$

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 $x=\frac{1}{2},\frac{3}{2}$