Question

Solve for X. "TexFormula1" title="log_{8} x-log_{8} (-2x+4) = log_{8} 3" alt="log_{8} x-log_{8} (-2x+4) = log_{8} 3" align="absmiddle" class="latex-formula">

Answer 1

Answer: $x=\frac{12}{7}$

Step-by-step explanation:

Remember the logarithms properties:

$log(m)-log(n)=log(\frac{m}{n})\\\\b^{log_b(a)}=a$

Then,simplifying:

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

Apply base 8 to boths sides and then solve for "x":

$8^{log_{8}(\frac{x}{-2x+4})}=8^{log_{8}(3)}\\\\\frac{x}{-2x+4}=3\\\\x=3(-2x+4)\\\\x=-6x+12\\x+6x=12\\7x=12\\\\x=\frac{12}{7}$

Answer 2

Answer:

x = 12/7.

Step-by-step explanation:

log8 x - log8 (-2x + 4) = log8 3

Using the law of logs, log a - log b = log (a/b):-

log8  [x / (-2x + 4)]  =  log8 3

Taking antilogs of both sides:

x / (-2x + 4) = 3

x = -6x + 12

7x = 12

x = 12/7

(answer).