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log-abc-a-2-and-log-abc-b-3-find-log-abc-c-




Question Number 207274 by hardmath last updated on 10/May/24
log_(abc)  a = 2   and   log_(abc)  b = 3  find:  log_(abc)  c = ?
$$\mathrm{log}_{\boldsymbol{\mathrm{abc}}} \:\mathrm{a}\:=\:\mathrm{2}\:\:\:\mathrm{and}\:\:\:\mathrm{log}_{\boldsymbol{\mathrm{abc}}} \:\mathrm{b}\:=\:\mathrm{3} \\ $$$$\mathrm{find}:\:\:\mathrm{log}_{\boldsymbol{\mathrm{abc}}} \:\mathrm{c}\:=\:? \\ $$
Answered by MM42 last updated on 10/May/24
log_(abc) a+log_(abc) b+log_(abc) c=1  ⇒log_(abc) c=−4 ✓
$${log}_{{abc}} {a}+{log}_{{abc}} {b}+{log}_{{abc}} {c}=\mathrm{1} \\ $$$$\Rightarrow{log}_{{abc}} {c}=−\mathrm{4}\:\checkmark \\ $$
Commented by hardmath last updated on 10/May/24
thank you dear professor
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{dear}\:\mathrm{professor} \\ $$

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