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LogarithmsQuestion and Answers: Page 1

Question Number 206303 Answers: 1 Comments: 0

log_2 4

$${log}_{\mathrm{2}} \mathrm{4} \\ $$

Question Number 205496 Answers: 1 Comments: 0

Question Number 204300 Answers: 1 Comments: 0

x^2 log_3 x^2 −(2x^2 +3)log_9 (2x+3)=3log_3 ((x/(2x+3)))

$${x}^{\mathrm{2}} \mathrm{log}_{\mathrm{3}} {x}^{\mathrm{2}} −\left(\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\mathrm{log}_{\mathrm{9}} \left(\mathrm{2}{x}+\mathrm{3}\right)=\mathrm{3log}_{\mathrm{3}} \left(\frac{{x}}{\mathrm{2}{x}+\mathrm{3}}\right) \\ $$

Question Number 204174 Answers: 1 Comments: 0

Question Number 203375 Answers: 0 Comments: 4

valeur x? (∡ECA =90)

$$\:\mathrm{valeur}\:\boldsymbol{\mathrm{x}}? \\ $$$$\left(\measuredangle\mathrm{ECA}\:\:=\mathrm{90}\right) \\ $$

Question Number 202172 Answers: 1 Comments: 0

If log_(12) 18 = A and log_(24) 54 = B then prove that AB + 5(A − B) = 1.

$$\mathrm{If}\:\mathrm{log}_{\mathrm{12}} \mathrm{18}\:=\:\mathrm{A}\:\mathrm{and}\:\mathrm{log}_{\mathrm{24}} \mathrm{54}\:=\:\mathrm{B}\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{AB}\:+\:\mathrm{5}\left(\mathrm{A}\:−\:\mathrm{B}\right)\:=\:\mathrm{1}. \\ $$

Question Number 202128 Answers: 0 Comments: 0

Question Number 200224 Answers: 3 Comments: 0

Question Number 199956 Answers: 1 Comments: 0

Question Number 199801 Answers: 1 Comments: 0

Question Number 198222 Answers: 1 Comments: 1

log _4 (5^x −3^x ) = log _5 (4^x +3^(x ) )

$$\:\:\:\mathrm{log}\:_{\mathrm{4}} \left(\mathrm{5}^{\mathrm{x}} −\mathrm{3}^{\mathrm{x}} \right)\:=\:\mathrm{log}\:_{\mathrm{5}} \left(\mathrm{4}^{\mathrm{x}} +\mathrm{3}^{\mathrm{x}\:} \right) \\ $$

Question Number 198124 Answers: 2 Comments: 0

solve for x log100+log(2+x)=10

$${solve}\:{for}\:{x}\:{log}\mathrm{100}+{log}\left(\mathrm{2}+{x}\right)=\mathrm{10} \\ $$

Question Number 197388 Answers: 4 Comments: 0

Question Number 197099 Answers: 2 Comments: 0

∫^( (π/2)) _( 0) ((ln(cost))/(sint)) dt=???

$$\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{cos}{t}\right)}{\mathrm{sin}{t}}\:\mathrm{d}{t}=??? \\ $$

Question Number 196690 Answers: 1 Comments: 0

If (ax)^(loga) = (bx)^(logb) then prove that x = (1/(ab)) .

$$\mathrm{If}\:\left({ax}\right)^{\mathrm{log}{a}} \:=\:\left({bx}\right)^{\mathrm{log}{b}} \:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${x}\:=\:\frac{\mathrm{1}}{{ab}}\:. \\ $$

Question Number 196683 Answers: 2 Comments: 0

If y = ((e^x − e^(− x) )/(e^x + e^(− x) )) then show that x = (1/2)log_e (((1 + y)/(1 − y))).

$$\mathrm{If}\:{y}\:=\:\frac{{e}^{{x}} \:−\:{e}^{−\:{x}} }{{e}^{{x}} \:+\:{e}^{−\:{x}} }\:\mathrm{then}\:\mathrm{show}\:\mathrm{that} \\ $$$${x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{log}_{{e}} \left(\frac{\mathrm{1}\:+\:{y}}{\mathrm{1}\:−\:{y}}\right). \\ $$

Question Number 196596 Answers: 0 Comments: 1

If f(x) = ln(((1 + x)/(1 − x))) then prove that f(((2x)/(1 + x^2 ))) = 2f(x).

$$\mathrm{If}\:{f}\left({x}\right)\:=\:\mathrm{ln}\left(\frac{\mathrm{1}\:+\:{x}}{\mathrm{1}\:−\:{x}}\right)\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that} \\ $$$${f}\left(\frac{\mathrm{2}{x}}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\:=\:\mathrm{2}{f}\left({x}\right). \\ $$

Question Number 196427 Answers: 1 Comments: 0

If f(x)=∫^( x) _( 0) (dt/(t+e^(−f(t)) )), determine f(x)

$$\mathrm{If}\:\:{f}\left({x}\right)=\underset{\:\mathrm{0}} {\int}^{\:{x}} \frac{{dt}}{{t}+{e}^{−{f}\left({t}\right)} },\:\mathrm{determine}\:{f}\left({x}\right) \\ $$

Question Number 196249 Answers: 0 Comments: 0

log_a x=30 log_b x=70 log_(ab) x=?

$${log}_{{a}} {x}=\mathrm{30} \\ $$$${log}_{{b}} {x}=\mathrm{70} \\ $$$${log}_{{ab}} {x}=? \\ $$

Question Number 196026 Answers: 1 Comments: 0

∫^( +∞) _( 0) (((lnt)^2 )/(1+t^2 ))dt

$$\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{\left({lnt}\right)^{\mathrm{2}} }{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 195895 Answers: 1 Comments: 0

Calcul ∫^( (π/2)) _( 0) t(√(tan(t))) dt

$$\mathrm{Calcul}\:\:\:\:\:\:\:\:\underset{\:\mathrm{0}} {\int}^{\:\frac{\pi}{\mathrm{2}}} \mathrm{t}\sqrt{\mathrm{tan}\left(\mathrm{t}\right)}\:\mathrm{dt} \\ $$

Question Number 195753 Answers: 1 Comments: 0

Calculer ∫^( 1) _( 0) ((ln^2 t)/( (√(1−t^2 ))))dt

$$\mathrm{Calculer}\:\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} \frac{{ln}^{\mathrm{2}} {t}}{\:\sqrt{\mathrm{1}−{t}^{\mathrm{2}} }}{dt} \\ $$

Question Number 195087 Answers: 2 Comments: 0

Question Number 194961 Answers: 1 Comments: 0

Question Number 194736 Answers: 0 Comments: 2

{: }

Question Number 194613 Answers: 2 Comments: 0

$$\:\:\:\:\:\:\cancel{\underline{ }} \\ $$

Question Number 194165 Answers: 1 Comments: 0

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