Question

Given log7=0.8451 and log2=0.3010 find the value of log28

Answer 1

\(28=2^2\times 7\) is a start

Answer 2

\[\log(28)=\log(4\times7)=\]

Answer 3

\[\log ab=\log a+\log b\]
\[\log c^n=n\log c\]

Answer 4

log(28)=log(28)?

Answer 5

that is step zero @Sukhvir ,
can you see the next steps as well...

Answer 6

log((28)(28))

Answer 7

log((784))

Answer 8

log(784) = 2.8943

Answer 9

You need to use the rules mentioned by @UnkleRhaukus here @Sukhvir
Factor 28
Then use the first property of logs mentioned by @UnkleRhaukus
Also @satellite73 has already factored 28 for you
\[28=2^2*7\]
So
\[\log(28)=\log(2^2 * 7)\]
Now apply that first property here:
\[\log(2^2 * 7)=\]

Answer 10

what is the first property? :S

Answer 11

that the logarithm of a product of factors is the sum of the logarithm of the factors
\[\log (a\times b)=\log (a)+\log (b)\]

Answer 12

loh(8)+log(7)

Answer 13

3log(2)+log(7)

Answer 14

\[\text{lol}(7\times8)=\text{lol}({56)}\]

Answer 15

\[\log(28)=\]

Answer 16

ugh i cant figure this out can you show me? my math skills are not strong

Answer 17

do you know how to factorise 28 ?

Answer 18

4*7

Answer 19

log(28)=log(4)+log(7)

Answer 20

good, can you also factorise 4

Answer 21

2*2

Answer 22

which can also be written (in index form) as....

Answer 23

2log(2)?

Answer 24

a*a = \(a\times a\) = a^2 = \(a^2\)

Answer 25

4 = 2*2 = 2 ^ ?

Answer 26

2^2

Answer 27

right ,
and the second rule of logs i wrote was

the log of a number raised to an index is the index multiplied by the log of the number
\[\log c^n=n\log c\]

so
\[\log(28)=\log(4)+\log(7)\]\[\quad\qquad=\log(2^2)+\log(7)\]\[\qquad\quad=\]\[\qquad\quad=\]

Answer 28

log(28)=1.748

Answer 29

nope

Answer 30

where did i go wrong?

Answer 31

i did log of 2^3 and then log7
and added them

Answer 32

if you dont want to learn the second rule thats fine just apply the first rule again
\[\log(28)=\log(4)+\log(7)=\log(2)+\log(2)+\log(7)\]

Answer 33

where did you get a three?

Answer 34

i missed read the power

Answer 35

ah well
\[\log 2^3+\log7=1.748\]
so the rest of your method worked

Answer 36

aha so i got 1.447 = log(28)?

Answer 37

thats good
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