Question

Given log 3=0.4471, log 5=0.699, log7=0.8451, log2=0.3010, find the value of
1.log 2.4

Answer 1

@terenzreignz

Answer 2

Oh logarithms, how they delight me :D

Answer 3

:W

Answer 4

Can you express 2.4 as a product/quotient of 3's, 2's and 5's ?

Answer 5

uhm,, i really don't understand,, :O

Answer 6

This takes creativity and/or getting used to.
\[\Large 2.4 = \frac{3\cdot 2^2}{5}\]

Answer 7

2.4 = 24/10, so log (2.4) = log (24/10) = log 24 - log 10 (we know that log 10 = 1)

All what we need is the log 24.

log (24) = log (2 x 2 x 2 x 3)
= log 2+ log 2 + log 2 + log 3
= 0.3010 + 0.3010 + 0.3010 + 0.4471
= 1.3501

Answer 8

@terenzreignz ,, how'd you come up with that?

Answer 9

You could have also said that log (24) = log(2^3 x 3) = log (2^3) + log 3
= 3log 2 + log 3
= 1.3501

Answer 10

experience... it's expressing 2.4 in terms of numbers that are useful to you, in this case, only 2's 3's 5's and 7's

Answer 11

okaaay,, then what??

Answer 12

See above.

Answer 13

Well, get the log.
\[\Large \log(2.4) = \log\left(\frac{3\cdot 2^2}{5}\right)\]

Answer 14

And then use the properties of logs, namely:
\[\Large \log(MN) = \log(M) + \log(N)\]\[\Large \log\left(\frac{M}{N}\right)=\log(M) - \log(N) \qquad N\ne 0\]\[\Large \log(M^p) = p\log(M)\]

Answer 15

wait, why is 2 squared and why is 5 a divisor?

Answer 16

It was arbitrary.... I mean come on...
\[\Large 2.4 = \frac{24}{10}= \frac{3\times 2\times2\times 2}{2\times 5}\]
do the cancellations yourself.

Answer 17

sorry,, it wasn't taught to us,

Answer 18

okay i get it

Answer 19

It's something you're already supposed to know... and it's called resourcefulness XD

You needed to find a way to reduce 2.4 into an expression with numbers you can actually use.. again, 2's, 3's, 5's and 7's are the only logs given to you, so use those.

Answer 20

log2+log4=log3+2log2-log5

Answer 21

log 3 + 2log2 - log 5 correct
log 2 + log 4....lacks the -log 5

:P

Answer 22

So your final answer?

Answer 23

why does it lack -log5?

Answer 24

kako... kulang ng -log 5 :P

log3 + log4 - log5 = log3 + 2log2 - log 5
:D

Answer 25

bakit nga, ehh log(2.4) lang

Answer 26

/hai/
\[\Large \log(2.4) = \log\left(\frac{3\cdot 4}{5}\right)=\log(3)+\log(4) - \log(5) \]okay? :P

Answer 27

okaaaay,,

Answer 28

akala ko kasi kasama si log(2.4)

Answer 29

next?

Answer 30

you already got it :/
log(3) + 2log(2) - log(5)

Answer 31

that's the answer??

Answer 32

Well, yes, actually :P

Just replace the log(3), log(2) and log(5) with their actual values and simplify ^_^

Answer 33

so i need calculator huh?

Answer 34

not really... but go ahead :D

Answer 35

how to simplify w/o calculator?

Answer 36

simple.
wag tamarin :P
0.4471 + 2(0.3010) - 0.699

Answer 37

aiyt,, ganun lang,,ahahahah