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Question Number 197250 Answers: 0 Comments: 0

log 3=a log 4=b log_5 36=?

$$\mathrm{log}\:\mathrm{3}={a} \\ $$$$\mathrm{log}\:\mathrm{4}={b} \\ $$$$\mathrm{lo}\underset{\mathrm{5}} {\mathrm{g}36}=?\: \\ $$

Question Number 197249 Answers: 3 Comments: 0

log_6 2=a log_6 9=?

$$\mathrm{lo}\underset{\mathrm{6}} {\mathrm{g}2}={a} \\ $$$$\mathrm{lo}\underset{\mathrm{6}} {\mathrm{g}9}=?\:\: \\ $$

Question Number 197248 Answers: 0 Comments: 3

a,b,c∈R ((a + 2b − 3ac)/(3ac)) = ((a + 4b − bc)/b) Find: ((2b)/a) − ((3a)/b)

$$\mathrm{a},\mathrm{b},\mathrm{c}\in\mathbb{R} \\ $$$$\frac{\mathrm{a}\:+\:\mathrm{2b}\:−\:\mathrm{3ac}}{\mathrm{3ac}}\:\:=\:\:\frac{\mathrm{a}\:+\:\mathrm{4b}\:−\:\mathrm{bc}}{\mathrm{b}} \\ $$$$\mathrm{Find}:\:\:\:\frac{\mathrm{2b}}{\mathrm{a}}\:−\:\frac{\mathrm{3a}}{\mathrm{b}} \\ $$

Question Number 197247 Answers: 1 Comments: 0

calcul ∫^( +∞) _( 0) ((ln(cht))/(sh(t)))dt

$$\mathrm{calcul}\:\underset{\:\mathrm{0}} {\int}^{\:+\infty} \frac{{ln}\left({cht}\right)}{{sh}\left({t}\right)}{dt} \\ $$

Question Number 197245 Answers: 0 Comments: 1

Question Number 197242 Answers: 0 Comments: 0

Question Number 197241 Answers: 0 Comments: 0

Question Number 197239 Answers: 1 Comments: 0

Question Number 197238 Answers: 0 Comments: 1

Question Number 197234 Answers: 1 Comments: 0

Question Number 197229 Answers: 2 Comments: 1

Question Number 197228 Answers: 1 Comments: 0

Question Number 197227 Answers: 0 Comments: 0

Question Number 197226 Answers: 1 Comments: 0

Question Number 197225 Answers: 1 Comments: 0

Question Number 197212 Answers: 0 Comments: 1

Is ∫f(x)dx=∫_0 ^x lim_(x→t) f(x)dt?

$$\mathrm{Is}\:\int{f}\left({x}\right){dx}=\int_{\mathrm{0}} ^{{x}} \underset{{x}\rightarrow{t}} {\mathrm{lim}}{f}\left({x}\right){dt}? \\ $$

Question Number 197196 Answers: 1 Comments: 0

Question Number 197194 Answers: 1 Comments: 0

Question Number 197191 Answers: 1 Comments: 0

∫(1/(x^3 −3x+7))dx

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{3}} −\mathrm{3}{x}+\mathrm{7}}{dx} \\ $$

Question Number 197190 Answers: 1 Comments: 2

∫_0 ^1 ^3 (√(1−x^7 )) dx − ∫^1 _0 ^7 (√(1−x^3 )) dx = ?

$$\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:^{\mathrm{3}} \sqrt{\mathrm{1}−{x}^{\mathrm{7}} }\:{dx}\:−\:\underset{\mathrm{0}} {\int}^{\mathrm{1}} \:^{\mathrm{7}} \sqrt{\mathrm{1}−{x}^{\mathrm{3}} }\:{dx}\:\:=\:\:? \\ $$

Question Number 197188 Answers: 1 Comments: 0

Question Number 197184 Answers: 1 Comments: 0

Show that log(−logi)=log((π/2))−i(π/2)

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{log}\left(−\mathrm{log}{i}\right)=\mathrm{log}\left(\frac{\pi}{\mathrm{2}}\right)−{i}\frac{\pi}{\mathrm{2}} \\ $$

Question Number 197185 Answers: 1 Comments: 0

Simplify (((((√2))^(√3) ∙((√3))^(√2) +((√2))^(√(12)) )/(((√6))^(√2) +((√2))^((√3)+(√2)) )))^(1/((√3)−(√2)))

$$\mathrm{Simplify} \\ $$$$\sqrt[{\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}}}]{\frac{\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}} \centerdot\left(\sqrt{\mathrm{3}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{12}}} }{\left(\sqrt{\mathrm{6}}\right)^{\sqrt{\mathrm{2}}} +\left(\sqrt{\mathrm{2}}\right)^{\sqrt{\mathrm{3}}+\sqrt{\mathrm{2}}} }} \\ $$

Question Number 197177 Answers: 0 Comments: 0

find ∫_0 ^(π/2) ln^2 (cosx)dx

$${find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} {ln}^{\mathrm{2}} \left({cosx}\right){dx} \\ $$

Question Number 197171 Answers: 1 Comments: 0

2^(log_3 (x^2 +1)) +2×(x^2 +1)^(log_3 2) =12 ⇒x=?

$$\mathrm{2}^{{log}_{\mathrm{3}} \left({x}^{\mathrm{2}} +\mathrm{1}\right)} +\mathrm{2}×\left({x}^{\mathrm{2}} +\mathrm{1}\right)^{{log}_{\mathrm{3}} \mathrm{2}} \:=\mathrm{12} \\ $$$$\Rightarrow{x}=? \\ $$$$ \\ $$

Question Number 197589 Answers: 1 Comments: 0

how many natural numbers with 4 different digits are divisible by 3?

$${how}\:{many}\:{natural}\:{numbers}\:{with}\:\mathrm{4} \\ $$$${different}\:{digits}\:{are}\:{divisible}\:{by}\:\mathrm{3}? \\ $$

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