Question

log 20 + log 50 - 2log 5 - 2log2

Answer 1

\[\log(a \times b) = \log (a) + \log(b)\]

Answer 2

log 20 times 50 times 4 over 25?

Answer 3

Break \(20\) with hammer into two parts..

Answer 4

?

Answer 5

20 = 4 times 5..

Answer 6

oh i thought you said 10 and 10

Answer 7

\[\log(20) = \log(4 \times 5)\]
Now use that formula..

Answer 8

One more formula you will need here:
\[\log(a^n) = n \cdot \log(a)\]

Answer 9

is it correct @ eta?

Answer 10

It is

Answer 11

\[\log(4 \times 5) = \log(4 ) + \log(5) = \log(2^2) + \log(5) = 2 \log(2) + \log(5)\]

Answer 12

Yes, you can go that way too, @SyedMohammed98

Answer 13

See, in my method, 2 log(2) and -2log(2) will cancel out..

Answer 14

@eta thanks for confusing me.

Answer 15

@SyedMohammed98 either you proceed or let me do this once, otherwise I know, asker will get confused for sure.
I let you do first..@SyedMohammed98, carry on..

Answer 16

i will just tell him the formula's log(a) + log(b) = log(a*b)
so log(20) + log(50) = log (20*50)
log(1000)
now the other one which is
log(a) - log(b) = log(a/b)
so log(5)/)log2)
take 2 common so it will be 2 ( (log5)/(log2) )
so if u join both u will get log(1000) - 2log( (log5/log2 )

Answer 17

can u continue from here @eta ...or u want to start ur method....

Answer 18

That will be log(5/2) only.. Yes syed?

Answer 19

\[2 \log(5) - 2 \log(2) = 2(\log(5) - \log(2) ) = 2 \log(\frac{5}{2})\]

Answer 20

I think my earlier method was good..

Answer 21

\[\log(20) = 2 \log(2) + \log(5)\]

Answer 22

\[\log(50) = \log( 25 \times 2) = \log(25) + \log(2) = \log(5^2) + \log(2) = 2 \log(5) + \log(2)\]

Answer 23

So, you are left with :
\[\implies \log(5) + \log(2) \implies \color{green}{\log(10)}\]

Answer 24

\(\large\color{blue}{ \displaystyle {\rm Log}(20)+ {\rm Log}(50)-2{\rm Log}(5)- 2{\rm Log}(2)}\)

\(\large\color{blue}{ \displaystyle {\rm Log}(2)+{\rm Log}(10)+ {\rm Log}(5)+{\rm Log}(10)-2{\rm Log}(5)- 2{\rm Log}(2)}\)

\(\large\color{blue}{ \displaystyle 2+{\rm Log}(2)+ {\rm Log}(5)-2{\rm Log}(5)- 2{\rm Log}(2)}\)

\(\large\color{blue}{ \displaystyle 2-{\rm Log}(5)- {\rm Log}(2)}\)

\(\large\color{blue}{ \displaystyle 2-{\rm Log}(5/2)}\)

\(\large\color{blue}{ \displaystyle 2-{\rm Log}(10/4)}\)

\(\large\color{blue}{ \displaystyle 2+{\rm Log}(4/10)}\)

\(\large\color{blue}{ \displaystyle 2+{\rm Log}(4)-{\rm Log}(10)}\)

\(\large\color{blue}{ \displaystyle 1+{\rm Log}(4)}\)

Answer 25

That is:
\[\log_a (a) = 1 \\ \log_{10}(10) = 1\]

Answer 26

eta, for the first line except a=1 or a=0

Answer 27

But our answer is not matching..

Answer 28

May be, I have left something..

Answer 29

or maybe I did

Answer 30

Yes, you must multiply them instead of divide..

Answer 31

\(\large\color{blue}{ \displaystyle 2-{\rm Log}(5)-{\rm Log}(2)}\)

\(\large\color{blue}{ \displaystyle 2-\left({\rm Log}(5)+{\rm Log}(2)\right)}\)

there is my mistake

Answer 32

\(2-1 =1\)

Answer 33

\(\large\color{blue}{ \displaystyle 2-\left({\rm Log}(5)+{\rm Log}(2)\right)}\)

\(\large\color{blue}{ \displaystyle 2-\left({\rm Log}(10)\right)}\)

ypu it is 1

Answer 34

yup*

Answer 35

i am so much confused.

Answer 36

you can also do it this way
if it has a pos put it on top
if it has a neg put it on bottom
this is what I mean
\[\log(\frac{20 \cdot 50}{5^2 \cdot 2^2})\]

Answer 37

\[\log(\frac{20}{2^2} \cdot \frac{50}{5^2})\]

Answer 38

you know 20/4=5
and 50/25=2

Answer 39

so you have log(5*2)

Answer 40

can you simplify log(5*2) further

Answer 41

log 10 which is 1

Answer 42

yep which is what @SolomonZelman got above somewhere

Answer 43

all I did was apply the following properties
log(a)+log(b)=log(ab)
log(m)-log(n)=log(m/n)
log(m^r)=r*log(m)
and finally you applied log_a(a)=1

Answer 44

\[\text{ Say you have something like this } \\ \log(4)-\log(3)-\log(2)+\log(4)-\log(6) \\ \text{ you can do that whole thingy I mentioned earlier } \\ \log (\frac{4 \cdot 4 }{3 \cdot 2 \cdot 6})\]
noticed if the log had a + in front of it the number went on the top inside
noticed if the log had a - in front of it the number went on the bottom inside

Answer 45

THANKS!