To solve this problem you must apply the proccedure shown below:
1- To solve the logarithm expression [tex] 2 log x = log 64 [/tex], you must apply the following properties:
[tex] alogx=logx^{a} [/tex]
[tex] logx-logy=log(x/y) [/tex]
[tex] a^{log(a)x}=x [/tex]
2-Keeping this on mind, you have:
[tex] log x^{2}-log 64=0\\ log(x^{2} /64)=0\\ 10^{log(x^{2} /64)} =10^{0} \\ x^{2} /64=1 [/tex]
3. Now, solve for [tex] x [/tex]:
[tex] x=\sqrt{64}\\ x=8, x=-8 [/tex]
4. If you susbtitute [tex] x=-8 [/tex] into the expression shown in the problem, you will see that it is invalid.
Therefore. the answer is: [tex] x=8 [/tex].
