Need Help on this question

Given that 2^x = 3^y = 6^z show that z = (xy)/(x+y). Teacher says that cannot use logarithms to solve, can only use indices to solve.

zz i too tired to work out. sighs. but i'll give u a clue.

6^z = (2^z)(3^z)

i'll try to check back tmr to see if u still need help

How come so long already no one do yet...?

2^x = 6^z => 2^(1/z) = 6^(1/x) ------ (1)
3^y = 6^z => 3^(1/z) = 6^(1/y) ------ (2)

(1) * (2):
2^(1/z) * 3^(1/z) = 6^(1/x) * 6^(1/y)
6^(1/z) = 6^(1/x + 1/y)

thus

1/z = 1/x + 1/y

rearranging

z = (xy)/(x+y)

just logged in Sad

Eagle, thanks for the solution.