Answer: [tex]x=-4.5[/tex]
Step-by-step explanation:
Add 2 to both sides of the equation and divide both sides of the equation by 15. Then:
[tex]15log_{8} (-2x-7)-2+2=3+2\\15log_{8} (-2x-7)=5\\\\\frac{15log_{8} (-2x-7)}{15}=\frac{5}{15}\\\\log_{8}(-2x-7)=\frac{1}{3}[/tex]
Apply base 8 to both sides of the equation:
[tex]8^{log_{8}(-2x-7)}=8^{\frac{1}{3}}\\\\-2x-7=8^{\frac{1}{3}}[/tex]
Solve for "x", then you get:
[tex]-2x-7=8^{\frac{1}{3}}\\\\-2x=\sqrt[3]{8}+7\\\\ x=\frac{\sqrt[3]{8}+7}{-2}\\\\x=-4.5[/tex]
