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Find-the-relation-between-x-and-y-if-log-4-x-3-log-27-y-




Question Number 159390 by pete last updated on 16/Nov/21
Find the relation between x and y if  log_4 x +3=log_(27) y
$$\mathrm{Find}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:{x}\:\mathrm{and}\:{y}\:\mathrm{if} \\ $$$$\mathrm{log}_{\mathrm{4}} {x}\:+\mathrm{3}=\mathrm{log}_{\mathrm{27}} {y} \\ $$
Answered by abdullah_ff last updated on 16/Nov/21
log_4 x+3=log_(27) y  ⇒ log_4 x=log_(27) y−3  ⇒ x=4^(log_(27) y−3)
$$\mathrm{log}_{\mathrm{4}} {x}+\mathrm{3}=\mathrm{log}_{\mathrm{27}} {y} \\ $$$$\Rightarrow\:\mathrm{log}_{\mathrm{4}} {x}=\mathrm{log}_{\mathrm{27}} {y}−\mathrm{3} \\ $$$$\Rightarrow\:{x}=\mathrm{4}^{\mathrm{log}_{\mathrm{27}} {y}−\mathrm{3}} \\ $$
Commented by pete last updated on 16/Nov/21
thank you sir
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{sir} \\ $$

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