Question

Help me ASAP please :( Type the correct answer in each box. Write your answers as fractions, using / as the fraction bar, and write the greater value first.

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the laws of logarithms

• log x - log y = log($\frac{x}{y}$)

• $log_{b}$ x = n ⇔ x = $b^{n}$

Hence

$log_{x}$( $\frac{8x-3}{4}$ ) = 2, hence

$\frac{8x-3}{4}$ = x² ( multiply both sides by 4 )

8x - 3 = 4x² ← rearrange into standard form

Subtract 8x - 3 from both sides

4x² - 8x  + 3 = 0 ← in standard form

(2x - 1)(2x - 3) = 0 ← in factored form

Equate each factor to zero and solve for x

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = $\frac{1}{2}$

2x - 3 = 0 ⇒ 2x = 3 ⇒ x = $\frac{3}{2}$