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zheka24 [161]
3 years ago
8

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

Mathematics
1 answer:
puteri [66]3 years ago
6 0

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}.

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