Question

Solve the logarithm. show steps.

Answer 1

`\log_82+\log_84x^2=1\\ D:4x^2>0\\ D:x\in\mathbb{R}\\ \log_88x^2=1\\ 8^1=8x^2\\ x^2=1\\ x=-1 \vee x=1\\`

Answer 2

`log_82+log_84x^2=1;\ D:x^2 > 0\Rightarrow x\\eq0\\\\log_8(2\cdot4x^2)=log_88^1\\\\log_88x^2=log_88\iff8x^2=8\ \ \ |both\ sides\ /:8\\\\x^2=1\iff x=-1\ or\ x=1.\\\\Solutions:x=-1\ \vee\ x=1.`