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VCE Stuff => VCE Mathematics => VCE Mathematics/Science/Technology => VCE Subjects + Help => VCE Mathematical Methods CAS => Topic started by: wildareal on September 18, 2010, 04:35:51 pm

Title: Proving Log Question
Post by: wildareal on September 18, 2010, 04:35:51 pm: Hi,

f(x)=3log(1+(x/2))

if f(u-2)+f(v-2)=f(auv+b), where u and v are positive real numbers, find the values of a and b.
Title: Re: Proving Log Question
Post by: 98.40_for_sure on September 18, 2010, 04:44:19 pm: $f(x)=3log(\frac{2+x}{2})$

$f(u-2)=3log(\frac{u}{2})$

$f(v-2)=3log(\frac{v}{2})$

$f(u-2)+ f(v-2)=3log(\frac{uv}{4})$

$f(auv+b)=3log(\frac{2+auv+b}{2})$

$3log(\frac{uv}{4})=3log(\frac{2+auv+b}{2})$

$\frac{uv}{4}=\frac{2+auv+b}{2}$

$2uv=8+4auv+4b$

Equating:

$2 = 4a \Rightarrow a=\frac{1}{2}$

$0 = 8 + 4b \Rightarrow b=-2$

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