anonymous
  • anonymous
if f(a.b)=f(a)+f(b) and f(2)=3, then f(32) equals ?
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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hartnn
  • hartnn
so, can you factor 32 in factors of 2 ?
anonymous
  • anonymous
It could b either 4.8 or 2.16
hartnn
  • hartnn
we have f(2) so we will select 2. 16 ok?

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hartnn
  • hartnn
so, f(32) = f(2*16) = f(2)+ f(16) got this ?
anonymous
  • anonymous
but what about 16 ? Should we break it too ?
hartnn
  • hartnn
absolutely!
hartnn
  • hartnn
16= 2* what ?
anonymous
  • anonymous
2*2*2*2 ?
hartnn
  • hartnn
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 ?
anonymous
  • anonymous
yeah. thanks alot :)
hartnn
  • hartnn
welcome ^_^ tell me what u get as f(32) if you want me to verify
anonymous
  • anonymous
15 ?
hartnn
  • hartnn
yes, i get 15 too :) correct!
anonymous
  • anonymous
\[ f(a\times b)=f(a)+f(b) \]Look familiar? \[ \ln(a\times b)=\ln(a)+\ln(b) \]
hartnn
  • hartnn
and bdw, @MissKhan \[ \begin{array}l\color{red}{\text{W}}\color{orange}{\text{E}}\color{#e6e600}{\text{L}}\color{green}{\text{C}}\color{blue}{\text{O}}\color{purple}{\text{M}}\color{purple}{\text{E}}\color{red}{\text{ }}\color{orange}{\text{t}}\color{#e6e600}{\text{o}}\color{green}{\text{ }}\color{blue}{\text{O}}\color{purple}{\text{P}}\color{purple}{\text{E}}\color{red}{\text{N}}\color{orange}{\text{S}}\color{#e6e600}{\text{T}}\color{green}{\text{U}}\color{blue}{\text{D}}\color{purple}{\text{Y}}\color{purple}{\text{!}}\color{red}{\text{!}}\color{orange}{\text{}}\end{array} \]
anonymous
  • anonymous
Yeah it looks familiar but am not allowed to use Calculator so ln is not appropriate.
anonymous
  • anonymous
Actually its: \[ \log_2(32) = \log_2(2^5) = 5 \]
anonymous
  • anonymous
@hartnn Thankyou. First experience to any site :)
anonymous
  • anonymous
Basically \(f(x) = 3\log_2(x)\)
hartnn
  • hartnn
nice! hope you enjoy learning and helping with openstudy! :) let me know if you need any help browsing this site....
anonymous
  • anonymous
So how are we suppose to get 15 by applying log ? nd without using calculator ?
anonymous
  • anonymous
@hartnn Suree:)
anonymous
  • anonymous
Actually, I'm just trying to show you an interseting way of looking at it. That is all.
hartnn
  • hartnn
wio just gave you an insight of what that function f could be, what we did is enough.
anonymous
  • anonymous
Math is all about noticing pattersn.
anonymous
  • anonymous
i dunno..
anonymous
  • anonymous
sorry
anonymous
  • anonymous
okay

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