Finding P

[Sam2756]

Hi

Please see below equatiin

(3/5)^3 x (9/15)^2 = (6/10)^p

How can I find the P, please help guys

 

[tkhunny]

Logarithms would make quick work of it.

The lesson may be to emphasize the use of exponents and your capacity to factor. Focus on 3/5, EVERYWHERE it appears.

 

[Sam2756]

So P =5

 

[tkhunny]

So P =5

It's usually considered bad form to change variables in the middle of a problem. P and p are not the same.

Other than that, I was hoping you would show your work.

 

[Otis]

So P =5

Hi Sam. Did you use the following property of exponents?

a^m · aⁿ = a^m+n

where your p is m+n.

?

 

[pka]

\((3/5)^3\times (9/15)^2 = (6/10)^p\)

Why not start by writing \(\dfrac{3^3}{5^3}\times\dfrac{3^4}{3^2\cdot 5^2}=\dfrac{2^p\cdot 3^p}{2^p\cdot 5^p}\)
Then we have \(\dfrac{3^5}{5^5}=\dfrac{3^p}{5^p}\) therefore \(p=~?\)