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




Question Number 146634 by mathdanisur last updated on 14/Jul/21
log_(xyz)  x = 2   and   log_(xyz)  y = 3  find   log_(xyz)  z = ?
$$\boldsymbol{{log}}_{\boldsymbol{{xyz}}} \:\boldsymbol{{x}}\:=\:\mathrm{2}\:\:\:{and}\:\:\:\boldsymbol{{log}}_{\boldsymbol{{xyz}}} \:\boldsymbol{{y}}\:=\:\mathrm{3} \\ $$$${find}\:\:\:\boldsymbol{{log}}_{\boldsymbol{{xyz}}} \:\boldsymbol{{z}}\:=\:? \\ $$
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  ⇒ log_(xyz) z = −4
$$\mathrm{log}_{{xyz}} {xyz}\:=\:\mathrm{1} \\ $$$$\mathrm{log}_{{xyz}} {x}+\mathrm{log}_{{xyz}} {y}+\mathrm{log}_{{xyz}} {z}\:=\:\mathrm{1} \\ $$$$\mathrm{2}+\mathrm{3}+\mathrm{log}_{{xyz}} {z}\:=\:\mathrm{1} \\ $$$$\Rightarrow\:\mathrm{log}_{{xyz}} {z}\:=\:−\mathrm{4} \\ $$
Commented by mathdanisur last updated on 14/Jul/21
cool thank you Ser
$${cool}\:{thank}\:{you}\:{Ser} \\ $$
Answered by nadovic last updated on 14/Jul/21
  log_(xyz)  xyz = log_(xyz) x+log_(xyz) y+log_(xyz) z                     1  =   2 + 3 + log_(xyz) z                   log_(xyz) z  = −4
$$\:\:\boldsymbol{{log}}_{\boldsymbol{{xyz}}} \:{xy}\boldsymbol{{z}}\:=\:{log}_{{xyz}} {x}+{log}_{{xyz}} {y}+{log}_{{xyz}} {z} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}\:\:=\:\:\:\mathrm{2}\:+\:\mathrm{3}\:+\:{log}_{{xyz}} {z} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{log}_{{xyz}} {z}\:\:=\:−\mathrm{4} \\ $$$$ \\ $$
Commented by mathdanisur last updated on 14/Jul/21
cool thanks Ser
$${cool}\:{thanks}\:{Ser} \\ $$

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