If 4^x =7^y =112^ z then prove that 2/X +1/y =1/z

Answer 1

112 = 16 * 7
x = log(112^z)/log4
y = log(112^z)/log7
1/x = log4/(z log112)
1/y = log7/(z log112)
2/x + 1/y = (log16 + log7)/(z log112) = log112/(z log112) = 1/z

Answer 2

I bet you mean ........ 4^x * 7^y =(4*4*7)^z = 4^2z * 7^z
looks like x= 2z and y = z
2/x + 1/y = 2/2z +1/z = 2/z