got his as a homework question and not sure if it is a misprint or this is the proper equation. Either way, got no clue how to proceed.

2^x = 5^y = 10^z

using logarithms to base 10 or otherwise, show that 1/z = 1/x + 1/y

i am thinking one of those equal signs is really a plus maybe a minus???

any help greatly appreciated.

jacs