Question

HELP!

Solve equation...
please show steps

Answer 1

`\log_25-\log_2(x+2)=3 \ \ \ \ \ \ [x\ \textgreater \ -2] \\ \\ \log_2 \left( (5)/(x+2)\right) =3 \\ \\ (5)/(x+2)=2^3 \\\\ (5)/(x+2)=8 \\ \\ 5=8(x+2) \\ \\ 5=8x+16 \\ \\ 5-16=8x \\ \\ -11=8x \\ \\ x=- (11)/(8)`

Answer 2

`\bf log_2(5)-log_2(x+2)=3\implies log_2\left( \cfrac{5}{x+2} \right)=3\\\\ -------------------------------\\\\ \textit{Logarithm Cancellation Rules}\\\\ log_a a^x\implies x\qquad \qquad \boxed{a^(log_ax)=x}\\\\ -------------------------------\\\\ 2^{log_2\left( (5)/(x+2) \right)}=2^3\implies \cfrac{5}{x+2}=2^3\implies \cfrac{5}{x+2}=8\implies 5=8x+16 \\\\\\ -11=8x\implies -\cfrac{11}{8}=x`