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

$${\mathit{l}\mathit{o}\mathit{g}}_{\mathit{x}\mathit{y}\mathit{z}}\mathit{x}=2and{\mathit{l}\mathit{o}\mathit{g}}_{\mathit{x}\mathit{y}\mathit{z}}\mathit{y}=3$$$$find{\mathit{l}\mathit{o}\mathit{g}}_{\mathit{x}\mathit{y}\mathit{z}}\mathit{z}=?$$

Answered by Olaf_Thorendsen last updated on 14/Jul/21

$${\log }_{xyz}xyz=1$$$${\log }_{xyz}x+{\log }_{xyz}y+{\log }_{xyz}z=1$$$$2+3+{\log }_{xyz}z=1$$$$\Rightarrow {\log }_{xyz}z=-4$$

Commented by mathdanisur last updated on 14/Jul/21

$$coolthankyouSer$$

Answered by nadovic last updated on 14/Jul/21

$${\mathit{l}\mathit{o}\mathit{g}}_{\mathit{x}\mathit{y}\mathit{z}}xy\mathit{z}={log}_{xyz}x+{log}_{xyz}y+{log}_{xyz}z$$$$1=2+3+{log}_{xyz}z$$$${log}_{xyz}z=-4$$$$$$

Commented by mathdanisur last updated on 14/Jul/21

$$coolthanksSer$$

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