3^x=5^y=15^-z find 1/x+1/y+1/z
Answers
Answered by
1
Answer:
Given 2^x=3^y=6^-z.
Lets assume that each and every term is equal to k. Which implies
2^x=k. Now by applying logarithm on both sides we get x=log k to base 2 and
1/x= log 2 to base k
And 3^y=k. Again by applying logarithm on both sides we get y=log k to base 3 and
1/y=log 3 to base k
Coming to third term we get 6^-z =k. Now by applying logarithm on both sides we get
- z=log k to base 6 which implies
z=-log k to base 6 and upon further simplification we get
Thus 1/z will be equal to - log 6 to base k.
Now upon adding 1/x+1/y+1/z will be equal to
log 2 to base k +log 3 to base k - log 6 to base k
Which will be equal to log 6 to base k - log 6 to base k. Thus makes the whole equation equal to zero.
Thus 1/x+1/y+1/z=0
Thank you :)
Similar questions