log-xyz-x-2-and-log-xyz-y-3-find-log-xyz-z-

Question Number 146634 by mathdanisur last updated on 14/Jul/21

{l o g}_{x y z} x = 2 a n d {l o g}_{x y z} y = 3

f i n d {l o g}_{x y z} z = ?

Answered by Olaf_Thorendsen last updated on 14/Jul/21

\log_{x y z} x y z = 1

\log_{x y z} x + \log_{x y z} y + \log_{x y z} z = 1

2 + 3 + \log_{x y z} z = 1

\Rightarrow \log_{x y z} z = - 4

Commented by mathdanisur last updated on 14/Jul/21

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Answered by nadovic last updated on 14/Jul/21

{l o g}_{x y z} x y z = {l o g}_{x y z} x + {l o g}_{x y z} y + {l o g}_{x y z} z

1 = 2 + 3 + {l o g}_{x y z} z

{l o g}_{x y z} z = - 4

Commented by mathdanisur last updated on 14/Jul/21

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