Question

How to solve this?

Answer 1

\[\LARGE (0.2)^{\log_\sqrt{5}} 0.2\]

Answer 2

I am not getting your question..

Answer 3

why?

Answer 4

What is in the power of 0.2??

Answer 5

log base root 5 (0.2)

Answer 6

\[\LARGE (0.2)^{{\log_\sqrt{5}} 0.2}\]

Answer 7

@waterineyes fixed

Answer 8

Yeah, I was not getting the last 0.2 part, now it is okay..

Answer 9

so now??

Answer 10

Wait..

Answer 11

Are your real name is Shivam, if I am not wrong then??

Answer 12

:O yes

Answer 13

Okay, I don't know how to proceed in an efficient way but I have two formulas with me, so let us try by using them:

\[\log_{a^{n}}N = \frac{1}{n} \cdot \log_a N\]

Answer 14

Shouldn't we consider changing bases?

Answer 15

If you know how to change the base then it is enough to solve it I think..
I don't know how to do that, can you please write the formula here??

Answer 16

@shubhamsrg who else?

Answer 17

@shubhamsrg

Answer 18

Maybe @Yahoo!

Answer 19

But how is changing the base gonna help anyway :/

Answer 20

Thank you thank you.

Answer 21

There is one more formula if we can reduce this to that, then we can solve this:

\[a^{\log_a{N}} = N\]

Answer 22

We have 0.2 below and if we can bring 0.2 in base, then we can easily solve this, but my mind is not working here that how can we do this..

@amistre64 , here moderator help required..

Answer 23

change of base is:\[log_{base}(arg)=\frac{ln(arg)}{ln(base)}\]
of course this works for any change and not just ln

Answer 24

Still this gives root 5
which is wrong

Answer 25

\[\LARGE (0.2)^{{\log_\sqrt{5}} (0.2)}=N\]
\[\LARGE {\log_\sqrt{5}} (0.2)=log_{0.2}(N)\]
\[\LARGE \frac{ln(0.2)}{\frac12ln(5)}=\frac{ln(N)}{ln(0.2)}\]
\[\LARGE 2\frac{(ln(0.2))^2}{ln(5)}=ln(N)\]
\[\LARGE exp(2\frac{(ln(0.2))^2}{ln(5)})=N \]

Answer 26

the answer is 2.

Answer 27

http://www.wolframalpha.com/input/?i=.2%5E%28log%28.2%29%2Flog%28sqrt%285%29%29%29

no, its should still be 25

Answer 28

or, youve asked the wrong question ...

Answer 29

okay,what if we had 0.5 instead of 0.2 ?

Answer 30

in the power