Question

Type the correct answer in each box. Write your answers as fractions, using / as the fraction bar, and write the greater value first.log (83–3)-log, 4 = 2the value of x isor

Answer 1

Given:

`\log _x(8x-3)-\log _x4=2\ldots\text{.}(1)`

As, it is known that,

`\begin{gathered} \log _ax-\log _ay=\log _a((x)/(y)) \\ \log _ab=m\Rightarrow b=a^m \end{gathered}`

Equation (1) can be written as,

`\begin{gathered} \log _x(8x-3)-\log _x4=2 \\ \text{log}_x((8x-3)/(4))=2 \\ (8x-3)/(4)=x^2 \\ 8x-3=4x^2 \\ 4x^2-8x+3=0 \\ \text{Compare it with ax}^2+bx+c=0 \\ a=4,b=-8,c=3 \\ x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{-(-8)\pm\sqrt[]{(-8)^2-48}}{2\cdot4} \\ x=(8\pm4)/(8) \\ x=(8+4)/(8),(8-4)/(8) \\ x=(3)/(2),(1)/(2) \end{gathered}`

Answer: 3/2 , 1/2