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
Say that,
2^x=t
5^y=t
10^z=t
Then,
x log 2=log t
y log 5=log t
z=log t
Thus,
1/z=1/log t
1/x=log 2/log t
1/y=log 5/log t
But,
1/x+1/y=log 5/log t+log 2/log t=(log 2+log 5)/log t
Note the numerator is the identity for logarithm product,
log (2*5)/log t=log 10/log t=1/log t=1/z
This is mine 26th post!!!