Question

I need help on a mathematics question. I need an explanation.

Answer 1

To solve this problem you must apply the proccedure shown below:

1- To solve the logarithm expression $2 log x = log 64$, you must apply the following properties:

$alogx=logx^{a}$

$logx-logy=log(x/y)$

$a^{log(a)x}=x$

2-Keeping this on mind, you have:

$log x^{2}-log 64=0\\ log(x^{2} /64)=0\\ 10^{log(x^{2} /64)} =10^{0} \\ x^{2} /64=1$

3. Now, solve for $x$:

$x=\sqrt{64}\\ x=8, x=-8$

4. If you susbtitute $x=-8$ into the expression shown in the problem, you will see that it is invalid.

Therefore. the answer is: $x=8$.