Question

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

Answer 1

you need to take the log of both sides, do you know how to do that?

Answer 2

yea so far i got square root of log of x log x = 8

Answer 3

then square both sides

Answer 4

to get rid of the root

Answer 5

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

Answer 6

well you made it harder on yourself let me explore this in details

Answer 7

\[\sqrt{\log_{10}(x) }=1/2\log_{10}(x) \]

Answer 8

do you agree

Answer 9

yes

Answer 10

so now we have

Answer 11

\[x ^{\frac{ 1 }{ 2 }\log_{10}(x) }=10^{8}\]

Answer 12

\[\log[x ^{\frac{ 1 }{ 2 }\log_{10}(x) }=10^{8}]\]

Answer 13

right and then is \[\frac{ 1}{ 2} (\log x )^2 \] ?

Answer 14

good

Answer 15

i think now you know how to do the rest

Answer 16

all you're left with is multiplying both side by 2 then taking the root of both sides

Answer 17

i get a different answer though , the book says the answer should be 10,000 :/

Answer 18

then the anti log

Answer 19

or log inverse

Answer 20

its not giving me the 10,000 :(

Answer 21

i got 10 000

Answer 22

ok i will show you the whole solution

Answer 23

but be patient because i am new to this editor

Answer 24

i am new too no worries thank you so much!

Answer 25

do you agree with this so far

Answer 26

\frac{ 1}{ 4} (\log x )^2

Answer 27

why do you square the 8?

Answer 28

\[\frac{ 1}{ 4} (\log x )^2=8^{2}\]

Answer 29

sorry

Answer 30

wait

Answer 31

i meant 16

Answer 32

because i wrote this on a paper

Answer 33

\[\ (\log x )^2=16\]

Answer 34

sorry again

Answer 35

\[\frac{ 1}{ 2} (\log x )^2 = 8\]

Answer 36

right

Answer 37

\[\ (\log x )^2=16\]

Answer 38

because we multiplied both side by 2

Answer 39

then we take the square root of both sides

Answer 40

that yields to

Answer 41

\[ (\log x )=4\]

Answer 42

got it !!! omg you are awesome thankss !!!!!!

Answer 43

you are welcome sorry for the mistakes its about 6 am my time

Answer 44

omg ! go to sleep!

Answer 45

where are you from?

Answer 46

UK

Answer 47

wow! well thanks again for all your help!

Answer 48

you are more than welcome at any time

Answer 49

well good luck :)

Answer 50

you too