Question

2. If 3^x=5^y=15^-z then show that 1/x+1/y+1/z=0

pls help
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Answer 1

Answer:

15^z = (3 x 5)^z = 3^z x 5^z (by exponents law)

= 3^z x 5^z = 3^x ………… (1)

& 3^z x 5^z = 5^y ………… (2)

(1) x (2) =

(3^z x 5^z)^2 = 3^x * 5^y

=> 3^(2z) * 5^(2z) = 3^x * 5^y

=> x = 2z ………. (3)

And y = 2z ……… (4)

By adding (3) & (4)

x + y = 4 z

=> z = (x+y)/ 4

Step-by-step explanation:

i hope it's helpful for you. ✌️