Question

given log 3 = 0.48 and log 7 = 0.84
calculate the value of log (0.30/0.7)

Answer 1

here's a hint that might help...

\[\huge \log a - \log b = \log (\frac ab )\]

does that give you any ideas?

Answer 2

uhm...what's huge and what's frac ab?

Answer 3

refresh your screen. you can't seem to see the latex

Answer 4

what's written there is

log a - log b = log (a/b)

Answer 5

let me give an example

log 6 = 2

log 4 = 3

then i want to find log (6/4) so i do:

log (6/4) = log 6 - log 4

so if i substitute the values i have...

log (6/4) = 2 - 3

so log (6/4) = -1

do you get the idea?

Answer 6

yeah, i know that, but then its 0.30 n 0.7....so what bout that?

Answer 7

do you agree that 0.30 is equal to 3/10 and 0.7 is equal to 7/10 ?

Answer 8

yes....i tried that, but still cudnt get it :(

Answer 9

so you know that 0.3 is 3/10 and 0.7 is 7/10

now here comes the magic

0.3/0.7 is equal to (3/10) / (7/10)

if you remember your algebra, you know that the denominator 10 would just cancel out. so you have 0.3/0.7 is equal to 3/7

Answer 10

but then u cant just cancel out 10..in logarithms i mean..

Answer 11

its just log3 - log7

Answer 12

u could

Answer 13

idk

Answer 14

hmm. we;; there would be another way to approach this

log (0.3) = log (3/10) = log 3 - log 10

log (0.7) = log (7/10) = log 7 - log 10

get the value of those two then find the difference of those differences

Answer 15

so,... (0.48 - 1) - (0.84 - 1)
so its bar1 . 48 - bar1.84
right?

Answer 16

yes..although i do not know what you mean by bar1

Answer 17

minus one....

Answer 18

the minus on top of the 1
-
1

Answer 19

so is the answer bar1.64?

Answer 20

let me try

Answer 21

unfortunately no. what did you do?

Answer 22

huh? what's the answer?

Answer 23

the answer should be negative.. since you're doing 0.48 - 1 and 0.84 - 1

Answer 24

ya then?

Answer 25

thats wat i said... negative one point 64

Answer 26

oh. bar means negative. anyway.. -1.64 is still not the answer.

0.48 - 1 is -0.52

0.84 - 1 is -0.36

subtract those two. remember that subtracting negative becomes positive (i.e. a - (-b) = a + b)

Answer 27

but there isnt a minus in logs...the minus either applies only for the characteristic or mantissa

Answer 28

who said logs cant have negatives?

let me give you an example

2^(-1) = 0.5

if you put that in log form

log_2 (0.5) = -1

Answer 29

the only time you can't have negatives is when you have log (-x) that's illegal since the base of that log is even and there's no exponent that can make an even number into a negative number

Answer 30

log(0.3/0.7)
= log(3/7)
= log3 - log7
= 0.48 - 0.84
= -0.36

log(0.3/0.7)
= log[ 3/10) / (7/10) ]
= log(3/10) - log(7/10)
= log3 - log10 - (log 7 - log10)
= log3 - log10 - log7 + log10
= log 3 - log7 + log10 - log10
= log3 - log7
= 0.48 - 0.84
= -0.36

Answer 31

well im getting the answer as bar1 point 64

Answer 32

bar 1 point 64 means -1 + 0.64 = -0.36, so you are correct

Answer 33

Oh.. :) thanks

Answer 34

wlcm