Question

x ^{sqrt{logx}}=10^{8}

Answer 1

\[x ^{\sqrt{\log_{10}x }}=10^8\]

Answer 2

Is that the problem?

Answer 3

Yes

Answer 4

Can you lead me through the problem?

Answer 5

Well, by inspection, we can figure out that x is 10^4. Can you see that?

Answer 6

Yes, I understand that but I do not know what to do after?

Answer 7

\[\sqrt{\log_{10}x }\log_{10}x=8 \]

Answer 8

So log10 x = 8?

Answer 9

Then if we square both sides we have:
\[\log_{10}x(\log_{10}x)^2=64 \]

Answer 10

\[(\log_{10}x )^3=64\]

Answer 11

Now take the third root of both sides:

Answer 12

\[\log_{10}x=4 \]

Answer 13

Now put it into its exponential form

Answer 14

Thank you so much!

Answer 15

yw