Solve for x. 15log_(8) (-2x-7)-2=3

Question

Solve for x.


`15log_(8) (-2x-7)-2=3`

Answer 1

Answer:
`x=-4.5`

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\\\\(15log_(8) (-2x-7))/(15)=(5)/(15)\\\\log_(8)(-2x-7)=(1)/(3)`

Apply base 8 to both sides of the equation:

`8^{log_(8)(-2x-7)}=8^{(1)/(3)}\\\\-2x-7=8^{(1)/(3)}`

Solve for "x", then you get:

`-2x-7=8^{(1)/(3)}\\\\-2x=\sqrt[3]{8}+7\\\\ x=\frac{\sqrt[3]{8}+7}{-2}\\\\x=-4.5`