SOLUTION: If {{{ (3^(4x+1) * 4^4 * 5^(2x+2)) / (81^(x-1) * 2^3 * 25^x) = 3^a * 6^b * 10^c }}} find the integer value of a + b + c

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: If {{{ (3^(4x+1) * 4^4 * 5^(2x+2)) / (81^(x-1) * 2^3 * 25^x) = 3^a * 6^b * 10^c }}} find the integer value of a + b + c      Log On


   

Question 864565: If find the integer value of a + b + c
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(3^(4x+1) * 4^4 * 5^(2x+2)) / (81^(x-1) * 2^3 * 25^x) =194400
194400 =3^a * 6^b * 10^c
194400 =2^5×3^5×5^2 prime factors
first take out all 10's =5 and matching 2
2*2×5*5=10^2
next take out all 2's and matching 3's ie 6's
3*3×3*2*2*2=6^3
and remaining 3's
3*3=3^2
(3^(4x+1) * 4^4 * 5^(2x+2)) / (81^(x-1) * 2^3 * 25^x) =3^2*6^3*10^2
a=2
b=3
c=2