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Question Number 23891 by ketto last updated on 09/Nov/17

Commented by math solver last updated on 09/Nov/17

write , 0.75 as ((75)/(100)) so by the properties of log , we can write log 75 − log 100 ⇒ log 3.5^2 − log 10^2 ⇒ log 3+ 2log5 − 2 ⇒ we know log 3= 0.4771 (you should remember it or else it should be given in q. as there is no proof of it i guess) ⇒ 0.4771 + 2(0.6990) −2 ⇒ − 0.124 . P.S : log ab = log a + log b. log(a/b) = log a − log b .

$$\mathrm{write}\:,\:\mathrm{0}.\mathrm{75}\:\mathrm{as}\:\frac{\mathrm{75}}{\mathrm{100}}\: \\ $$$$\mathrm{so}\:\mathrm{by}\:\mathrm{the}\:\mathrm{properties}\:\mathrm{of}\:\mathrm{log}\:, \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{write}\: \\ $$$$\mathrm{log}\:\mathrm{75}\:−\:\mathrm{log}\:\mathrm{100}\: \\ $$$$\Rightarrow\:\mathrm{log}\:\mathrm{3}.\mathrm{5}^{\mathrm{2}} \:−\:\mathrm{log}\:\mathrm{10}^{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{log}\:\mathrm{3}+\:\mathrm{2log5}\:\:−\:\mathrm{2} \\ $$$$\Rightarrow\:\mathrm{we}\:\mathrm{know}\:\mathrm{log}\:\mathrm{3}=\:\mathrm{0}.\mathrm{4771}\:\left(\mathrm{you}\:\mathrm{should}\right. \\ $$$$\mathrm{remember}\:\mathrm{it}\:\mathrm{or}\:\mathrm{else}\:\mathrm{it}\:\mathrm{should}\:\mathrm{be}\:\mathrm{given} \\ $$$$\left.\mathrm{in}\:\mathrm{q}.\:\mathrm{as}\:\mathrm{there}\:\mathrm{is}\:\mathrm{no}\:\mathrm{proof}\:\mathrm{of}\:\mathrm{it}\:\mathrm{i}\:\mathrm{guess}\right) \\ $$$$\Rightarrow\:\mathrm{0}.\mathrm{4771}\:+\:\mathrm{2}\left(\mathrm{0}.\mathrm{6990}\right)\:−\mathrm{2}\: \\ $$$$\Rightarrow\:\:−\:\:\mathrm{0}.\mathrm{124}\:. \\ $$$$\mathrm{P}.\mathrm{S}\::\:\mathrm{log}\:\mathrm{ab}\:=\:\mathrm{log}\:\mathrm{a}\:+\:\mathrm{log}\:\mathrm{b}. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{log}\frac{\mathrm{a}}{\mathrm{b}}\:=\:\mathrm{log}\:\mathrm{a}\:−\:\mathrm{log}\:\mathrm{b}\:. \\ $$$$ \\ $$

Commented by mrW1 last updated on 09/Nov/17

if log 2 is given, then there is no need to give log 5, since log 2 +log 5=1. so the question is strange. The question could be: Given log 2=0.3010 and log 3=0.4771 Evaluate log 0.75

$${if}\:\mathrm{log}\:\mathrm{2}\:{is}\:{given},\:{then}\:{there}\:{is}\:{no} \\ $$$${need}\:{to}\:{give}\:\mathrm{log}\:\mathrm{5},\:{since}\:\mathrm{log}\:\mathrm{2}\:+\mathrm{log}\:\mathrm{5}=\mathrm{1}. \\ $$$${so}\:{the}\:{question}\:{is}\:{strange}.\: \\ $$$$ \\ $$$${The}\:{question}\:{could}\:{be}: \\ $$$${Given}\:\mathrm{log}\:\mathrm{2}=\mathrm{0}.\mathrm{3010}\:{and}\:\mathrm{log}\:\mathrm{3}=\mathrm{0}.\mathrm{4771} \\ $$$${Evaluate}\:\mathrm{log}\:\mathrm{0}.\mathrm{75} \\ $$

Commented by math solver last updated on 09/Nov/17

exactly ! that′s what i want to convey.

$$\mathrm{exactly}\:!\:\mathrm{that}'\mathrm{s}\:\mathrm{what}\:\mathrm{i}\:\mathrm{want}\:\mathrm{to}\:\mathrm{convey}. \\ $$$$ \\ $$

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