if 2^x=3^y=6^-z find the value of 1/x+1/y+1/z ​

Question

if 2^x=3^y=6^-z
find the value of 1/x+1/y+1/z

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Faith 4 weeks 2021-08-19T02:35:35+00:00 2 Answers 0 views 0

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    0
    2021-08-19T02:36:51+00:00

    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 🙂

    0
    2021-08-19T02:37:19+00:00

    Answer:

    0

    Step-by-step explanation:

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