Question

if 2^x= 5^y= 10^z, then prove that 1/x + 1/y = 1/z​

Answer 1

Step-by-step explanation:

let us assume that 2^x= 5^y= 10^z=k

let us assume that 2^x= 5^y= 10^z=kthen,

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/z

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand2×5=10

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand2×5=10so according to question

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand2×5=10so according to questionk^1/x × k^1/y = k^1/z

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand2×5=10so according to questionk^1/x × k^1/y = k^1/zso same base is equal powers

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand2×5=10so according to questionk^1/x × k^1/y = k^1/zso same base is equal powers1/x + 1/y = 1/z

let us assume that 2^x= 5^y= 10^z=kthen, 2^x= k^1/x5^y=k^1/y10^z=k^1/zand2×5=10so according to questionk^1/x × k^1/y = k^1/zso same base is equal powers1/x + 1/y = 1/z hence proved

Answer 2

I don't know the answer