Question

x^Sqroot log x= 10^8

Answer 1

\[\large x^{\sqrt{\log(x)}}=10^8\]?

Answer 2

Yes thats correct

Answer 3

hmmm
is that log base ten?

Answer 4

yeah

Answer 5

i guess you could start by taking the log base ten of both sides and get
\[\log(x^{\sqrt{\log(x)}})=8\]

Answer 6

or
\[\sqrt{\log(x)}\log(x)=8\]

Answer 7

yeah ive gotten that far, i just dont know what to do next

Answer 8

yeah me neither

Answer 9

Darn I was hoping this site would help :(

Answer 10

maybe write it as
\[\log(x)^{\frac{3}{2}}=8\]

Answer 11

that should make it easier, since you solve
\[u^{\frac{3}{2}}=8\] via
\[u=8^{\frac{2}{3}}=2^2=4\]

Answer 12

making
\[\log(x)=4\] which, in equivalent exponential form, is \(x=10^4\)

Answer 13

i wonder if we could have seen that from the start...

Answer 14

So... What would be your ending answer?

Answer 15

that would be it \(10^4\)
want to check it?

Answer 16

yeah thats correct. But you kind of lost me when u said u^3/2=8

Answer 17

is it clear how i went from
\[\sqrt{\log(x)}\log(x)\] to
\[\left(\log(x)\right)^{\frac{3}{2}}\]

Answer 18

No sorry

Answer 19

i added the exponents
\[\sqrt{u}=u^{\frac{1}{2}}\] so
\[\sqrt{u}\times u=u^{\frac{3}{2}}\]

Answer 20

Oh I understand

Answer 21

So now I am at log x ^3/2 =8

Answer 22

then to solve for \(\log(x)\) take the cubed root of both sides, you get
\[(\log(x))^{\frac{1}{2}}=2\] then square both sides and get
\[\log(x)=4\]

Answer 23

U are a genius, Thank you so much

Answer 24

Do you get paid to do this?

Answer 25

i get $10 for every answer
$20 for each correct one

Answer 26

seriously? how do u sign up for that job

Answer 27

and how do they keep track if you get it right or not?