Question

Solve for x. -7)-2=3" alt="15log_{8} (-2x-7)-2=3" align="absmiddle" class="latex-formula">

Answer 1

Answer: $x=-4.5$

Step-by-step explanation:

Add 2 to both sides of the equation and divide both sides of the equation by 15. Then:

$15log_{8} (-2x-7)-2+2=3+2\\15log_{8} (-2x-7)=5\\\\\frac{15log_{8} (-2x-7)}{15}=\frac{5}{15}\\\\log_{8}(-2x-7)=\frac{1}{3}$

Apply base 8 to both sides of the equation:

$8^{log_{8}(-2x-7)}=8^{\frac{1}{3}}\\\\-2x-7=8^{\frac{1}{3}}$

Solve for "x", then you get:

$-2x-7=8^{\frac{1}{3}}\\\\-2x=\sqrt[3]{8}+7\\\\ x=\frac{\sqrt[3]{8}+7}{-2}\\\\x=-4.5$