Question

5^x=3^y=45^z. then prove


that 1/z=1/x+2/y

Answer 1

Heya!

5^x = 3^y = 45^z = k ( Suppose )

5^x = k

5 = k^(1/x) ... Equation ( i )

3^y = k

3 = k^(1/y) ... Equation ( ii )

(45)^z = k

45 = k^(1/z) ... Equation ( iii )

=>

45 = k^(1/z)

3² × 5 = k^(1/z)

k^(2/y ) × k^(1/x) = k^(1/z)

k^( 2/y + 1/x ) = k^(1/z )

2/y + 1/x = 1/z

1/z = 2/y + 1/x

HENCE, PROVED.