Question

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

Answer 1

Answer:

Final answer is $\frac{3}{2}$ or $\frac{1}{2}$.

Step-by-step 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 $\log_c\left(A\right)-\log_c\left(B\right)=\log_c\left(\frac{A}{B}\right)$

$\log_x\left(\frac{8x-3}{4}\right)=2$

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

$x^2=\frac{8x-3}{4}$

$4x^2=8x-3$

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

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

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

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

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

$2x=3$ or $2x=1$

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

Hence final answer is $\frac{3}{2}$ or $\frac{1}{2}$.