Answer: [tex]x=\frac{12}{7}[/tex]
Step-by-step explanation:
Remember the logarithms properties:
[tex]log(m)-log(n)=log(\frac{m}{n})\\\\b^{log_b(a)}=a[/tex]
Then,simplifying:
[tex]log_{8}(\frac{x}{-2x+4}) = log_{8}(3)[/tex]
Apply base 8 to boths sides and then solve for "x":
[tex]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}[/tex]
