Question

if f(a.b)=f(a)+f(b) and f(2)=3, then f(32) equals ?

Answer 1

so,
can you factor 32 in factors of 2 ?

Answer 2

It could b either 4.8 or 2.16

Answer 3

we have f(2)
so we will select 2. 16 ok?

Answer 4

so, f(32) = f(2*16) = f(2)+ f(16)
got this ?

Answer 5

but what about 16 ? Should we break it too ?

Answer 6

absolutely!

Answer 7

16= 2* what ?

Answer 8

2*2*2*2 ?

Answer 9

so, we go like this, step by step,
f(32) = f(16) +f(2)

but f(16) = f(8*2)= f(8)+f(2)

so f(32)= f(8)+f(2)+ f(2)

got this ?
can u continue ?

Answer 10

yeah. thanks alot :)

Answer 11

welcome ^_^
tell me what u get as f(32) if you want me to verify

Answer 12

15 ?

Answer 13

yes, i get 15 too :)
correct!

Answer 14

\[
f(a\times b)=f(a)+f(b)
\]Look familiar? \[
\ln(a\times b)=\ln(a)+\ln(b)
\]

Answer 15

and bdw,
@MissKhan
\[ \begin{array}l\color{red}{\text{W}}\color{orange}{\text{E}}\color{#e6e600}{\text{L}}\color{green}{\text{C}}\color{blue}{\text{O}}\color{purple}{\text{M}}\color{purple}{\text{E}}\color{red}{\text{ }}\color{orange}{\text{t}}\color{#e6e600}{\text{o}}\color{green}{\text{ }}\color{blue}{\text{O}}\color{purple}{\text{P}}\color{purple}{\text{E}}\color{red}{\text{N}}\color{orange}{\text{S}}\color{#e6e600}{\text{T}}\color{green}{\text{U}}\color{blue}{\text{D}}\color{purple}{\text{Y}}\color{purple}{\text{!}}\color{red}{\text{!}}\color{orange}{\text{}}\end{array} \]

Answer 16

Yeah it looks familiar but am not allowed to use Calculator so ln is not appropriate.

Answer 17

Actually its: \[
\log_2(32) = \log_2(2^5) = 5
\]

Answer 18

@hartnn Thankyou. First experience to any site :)

Answer 19

Basically \(f(x) = 3\log_2(x)\)

Answer 20

nice! hope you enjoy learning and helping with openstudy! :)

let me know if you need any help browsing this site....

Answer 21

So how are we suppose to get 15 by applying log ? nd without using calculator ?

Answer 22

@hartnn Suree:)

Answer 23

Actually, I'm just trying to show you an interseting way of looking at it. That is all.

Answer 24

wio just gave you an insight of what that function f could be,
what we did is enough.

Answer 25

Math is all about noticing pattersn.

Answer 26

i dunno..

Answer 27

sorry

Answer 28

okay