Two equations two variables....easy ?

Algebra Level 3

If 3^x = 25y and 5^x = 9y then what is the value of (y-x) ?

Given: (a) is the floor function

NOTE : This problem is original. :P

2 3 0 1

Gaurav Sharma by Gaurav Sharma , 24, India

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1 solution

Parveen Soni
Nov 13, 2014

Take log (base 10) both sides on both given equations we have
x log 3=2 log 5+log y -----(1)
x log 5=2 log 3+log y -------(2) on solving 1 & 2
x=-2 and y=1/225
now floor(1/225-(-2))=floor(2.004444444)=2

1 Helpful 0 Interesting 0 Brilliant 0 Confused

3^x = 25y => y = (3^x)/25 Divide 1 equation on 2 one. (3^x)/(5^x)=25/9 => (3^x)/(5^x) = (5/3)^2 => (3/5)^x=(5/3)^2 => (5/3)^(-x)=(5/3)^2 => x =-2 =>y-x=2 + (1/(9 * 25)) or floor of it is 2.

Alex Gawkins - 6 years, 7 months ago

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