Question

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

Answer 1

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

Answer 2

how does 8log10 = 8?

Answer 3

what are we doing here? just solving for x?

Answer 4

yeah without using a calculator

Answer 5

that is because log (10) = 1, when there is no base, its understood to be base 10

Answer 6

but ten wasn't the base

Answer 7

then what is the base? you gotta put it or else people will think its 10

Answer 8

ok sorry let me show you where i got to

Answer 9

\[\left( \sqrt{logx} \right)\left( logx \right)=10^{8}\]

Answer 10

\[=8\log10\]

Answer 11

Right. So you are taking the log (base 10) of both sides of the equation. the right hand side simplifies to 8

Answer 12

So you should have:
\[\sqrt{\log(x)}*\log(x) = 8\]

Answer 13

does it simplify because since the logs base is ten and since its \[8log _{10}10\] thelog simplifies to 1?

Answer 14

Right :)

Answer 15

ohhhh thanks see i knew the base of log was ten but i didnt know that i could do that thanks!!

Answer 16

So do you have an idea of where to go from here?

Answer 17

yes!

Answer 18

cool, have fun :)