Question

\[\LARGE \log(\log x)+\log(\log x^5-4)=0\]
A) x=1
B) x=-1
C) x=-2
D) x=0

Answer 1

let log x = u

Answer 2

... let me see what I can do. :)

Answer 3

but then ...
\[\LARGE \log(u)+\log(5u-4)=0\]
\[\LARGE \log(5u^2-4u)=0\]
now according to:
\[\LARGE \log_ab=c \quad \Longrightarrow b=a^c\]
I thought about:
\[\LARGE 5u^2-4u=10^0\]
\[\LARGE 5u^2-4u-1=0\]
\[\LARGE u_{1/2}=\frac{4\pm\sqrt{16-20\cdot (-1)}}{10}\]
\[\LARGE u_{1/2}=\frac{4\pm6}{10}\]
\[\LARGE u_1=1 \quad \quad ,\quad \quad u_2=-\frac25\]
so...
\[\LARGE \log x=1 \Longrightarrow x=10\]
and
\[\LARGE \log x=-\frac25 \Longrightarrow x=\frac{1}{\sqrt[5]{100}}\]
... O_O

Answer 4

sorry.. it's -1/5
\[\LARGE x=\frac{1}{\sqrt[5]{10}}\]

Answer 5

@satellite73 since you love logs :P , please can you have a look what I'm doing wrong :(

Answer 6

http://www.wolframalpha.com/input/?i=solve+log%5B10%2C+log+%5B10%2C+x%5D%5D+%2B+log%5B10%2C+%28log%5B10%2C+x%5E5%5D+-+4%29%5D

Answer 7

why it says "e" to me ! ?:O http://www.wolframalpha.com/input/?i=+log%28log+x%29%2Blog%28log+x%5E5-4%29%3D0

Answer 8

use this
log[10, x]

Answer 9

but it says there that is in base 10 !... it doesn't matter, I don't know if my PC went crazy, but your link doesn't show a solution or something. O_O , :( ..@experimentX :)

Answer 10

your method is right .. I think so.

Answer 11

but my options... :(

Answer 12

put this on wolfram alpha.
solve log[10, log [10, x]] + log[10, (log[10, x^5] - 4)]

Answer 13

x=10 ? :O

Answer 14

No.

Answer 15

then how... can you provide a better solution, that's what I'm looking for.

Answer 16

@Mertsj

Answer 17

Wolf says 2.80688

Answer 18

So based on the posted problem and the posted answers, I'd say there is an error in the posting.

Answer 19

Make sure when you type it into wolf that you use the base 10 option.

Answer 20

ok hold on a second...

Answer 21

Question Nr. 7

Answer 22

Well, just try replacing x with each of those answers. Which one works?

Answer 23

Every single one of them results in a negative argument in log(x^5-4)

Answer 24

I don't know :( I'm pretty lost
\[\LARGE \log_{10}(0)=?\]
since:
\[\LARGE \log_ab \quad\quad \quad ,\quad \quad b>0\]
so I guess it can't be option D :O

Answer 25

10^0=1 but 10 ^x cannot be 0

Answer 26

log 0 is undefined.

Answer 27

I see this is in a foreign language. Perhaps the notation means something different. Why do you need to do this problem anyway?

Answer 28

just to exercise , nothing special ^_^ ... It's ok, I'll ask my professor probably there's a mistake in the book. ;) Thanks for the help @Mertsj @experimentX

Answer 29

yw

Answer 30

yw When you find out, you might enlighten us as well.

Answer 31

lol , ok. Although I'm sure there must be a mistake ;) . Have a nice day .