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Question Number 70252 Answers: 1 Comments: 0

If, log x^y = 6 and log 14x^(8y) = 3 then find the value of x, y.

$$\mathrm{If},\:\mathrm{log}\:\mathrm{x}^{\mathrm{y}} \:=\:\mathrm{6}\:\mathrm{and}\:\mathrm{log}\:\mathrm{14x}^{\mathrm{8y}} \:=\:\mathrm{3}\:\mathrm{then}\:\mathrm{find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x},\:\mathrm{y}. \\ $$

Question Number 70287 Answers: 0 Comments: 2

I wanted to say this earlier... I love mathematics and I also love people. But I′m not here to solve the same old boring problems copied from facebook or whatsapp or other platforms. They are not interesting at all. They have been coming in as a kind of competition, or simply to brag, they′ve been traded from one non−mathematician to the other. No use to copy−paste problems that you found somewhere on the web and that you might not even be able to fully understand. If you need an explanation, you′re welcome, but I won′t do your homework and I won′t answer impolite posts. Last but not least: I won′t try to solve the famous unsolved problems much better people were not able to cope with.

$$\mathrm{I}\:\mathrm{wanted}\:\mathrm{to}\:\mathrm{say}\:\mathrm{this}\:\mathrm{earlier}... \\ $$$$\mathrm{I}\:\mathrm{love}\:\mathrm{mathematics}\:\mathrm{and}\:\mathrm{I}\:\mathrm{also}\:\mathrm{love}\:\mathrm{people}. \\ $$$$\mathrm{But}\:\mathrm{I}'\mathrm{m}\:\mathrm{not}\:\mathrm{here}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{same}\:\mathrm{old}\:\mathrm{boring} \\ $$$$\mathrm{problems}\:\mathrm{copied}\:\mathrm{from}\:\mathrm{facebook}\:\mathrm{or}\:\mathrm{whatsapp} \\ $$$$\mathrm{or}\:\mathrm{other}\:\mathrm{platforms}.\:\mathrm{They}\:\mathrm{are}\:\mathrm{not}\:\mathrm{interesting} \\ $$$$\mathrm{at}\:\mathrm{all}.\:\mathrm{They}\:\mathrm{have}\:\mathrm{been}\:\mathrm{coming}\:\mathrm{in}\:\mathrm{as}\:\mathrm{a}\:\mathrm{kind} \\ $$$$\mathrm{of}\:\mathrm{competition},\:\mathrm{or}\:\mathrm{simply}\:\mathrm{to}\:\mathrm{brag},\:\mathrm{they}'\mathrm{ve} \\ $$$$\mathrm{been}\:\mathrm{traded}\:\mathrm{from}\:\mathrm{one}\:\mathrm{non}−\mathrm{mathematician} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{other}. \\ $$$$ \\ $$$$\mathrm{No}\:\mathrm{use}\:\mathrm{to}\:\mathrm{copy}−\mathrm{paste}\:\mathrm{problems}\:\mathrm{that}\:\mathrm{you} \\ $$$$\mathrm{found}\:\mathrm{somewhere}\:\mathrm{on}\:\mathrm{the}\:\mathrm{web}\:\mathrm{and}\:\mathrm{that}\:\mathrm{you} \\ $$$$\mathrm{might}\:\mathrm{not}\:\mathrm{even}\:\mathrm{be}\:\mathrm{able}\:\mathrm{to}\:\mathrm{fully}\:\mathrm{understand}. \\ $$$$ \\ $$$$\mathrm{If}\:\mathrm{you}\:\mathrm{need}\:\mathrm{an}\:\mathrm{explanation},\:\mathrm{you}'\mathrm{re}\:\mathrm{welcome}, \\ $$$$\mathrm{but}\:\mathrm{I}\:\mathrm{won}'\mathrm{t}\:\mathrm{do}\:\mathrm{your}\:\mathrm{homework}\:\mathrm{and}\:\mathrm{I}\:\mathrm{won}'\mathrm{t} \\ $$$$\mathrm{answer}\:\mathrm{impolite}\:\mathrm{posts}. \\ $$$$ \\ $$$$\mathrm{Last}\:\mathrm{but}\:\mathrm{not}\:\mathrm{least}:\:\mathrm{I}\:\mathrm{won}'\mathrm{t}\:\mathrm{try}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the} \\ $$$$\mathrm{famous}\:\mathrm{unsolved}\:\mathrm{problems}\:\mathrm{much}\:\mathrm{better} \\ $$$$\mathrm{people}\:\mathrm{were}\:\mathrm{not}\:\mathrm{able}\:\mathrm{to}\:\mathrm{cope}\:\mathrm{with}. \\ $$

Question Number 70232 Answers: 0 Comments: 3

Solve xy′ − y sin x + y^5 = 0

$$\mathrm{Solve} \\ $$$${xy}'\:−\:{y}\:\mathrm{sin}\:{x}\:+\:{y}^{\mathrm{5}} \:=\:\mathrm{0} \\ $$

Question Number 70230 Answers: 0 Comments: 2

Question Number 70219 Answers: 0 Comments: 1

Question Number 70296 Answers: 1 Comments: 1

Question Number 70225 Answers: 1 Comments: 3

Question Number 70198 Answers: 1 Comments: 0

Question Number 70197 Answers: 0 Comments: 1

Question Number 70196 Answers: 1 Comments: 0

Question Number 70216 Answers: 0 Comments: 0

let A = (((1 −1)),((1 2)) ) 1)calculate A^n 2) find e^A and e^(−A)

$${let}\:{A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\:−\mathrm{1}}\\{\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix} \\ $$$$\left.\mathrm{1}\right){calculate}\:{A}^{{n}} \:\:\:\:\: \\ $$$$\left.\mathrm{2}\right)\:{find}\:{e}^{{A}} \:{and}\:{e}^{−{A}} \\ $$

Question Number 70237 Answers: 0 Comments: 3

calculate ∫_0 ^∞ ((xsin(αx))/(1+x^4 ))dx with α real

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\alpha{x}\right)}{\mathrm{1}+{x}^{\mathrm{4}} }{dx}\:{with}\:\alpha\:{real} \\ $$

Question Number 70298 Answers: 1 Comments: 0

Question Number 70168 Answers: 1 Comments: 3

Question Number 70167 Answers: 0 Comments: 1

find minima of (x_1 −x_2 )^2 +5+(√(1−(x_1 )^2 ))+(√(4x_2 )) ∀ x_1 ,x_2 ∈R

$${find}\:{minima}\:{of} \\ $$$$\left({x}_{\mathrm{1}} −{x}_{\mathrm{2}} \right)^{\mathrm{2}} +\mathrm{5}+\sqrt{\mathrm{1}−\left({x}_{\mathrm{1}} \right)^{\mathrm{2}} }+\sqrt{\mathrm{4}{x}_{\mathrm{2}} }\:\:\forall\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} \in{R} \\ $$

Question Number 70163 Answers: 1 Comments: 0

Question Number 70162 Answers: 1 Comments: 0

Question Number 70161 Answers: 1 Comments: 0

Question Number 70159 Answers: 1 Comments: 1

Question Number 70150 Answers: 0 Comments: 1

prove that ∫_0 ^(π/2) (√((4−sin^2 x)))dx < ((π(√(14)))/4)

$${prove}\:{that}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \sqrt{\left(\mathrm{4}−{sin}^{\mathrm{2}} {x}\right)}{dx}\:<\:\frac{\pi\sqrt{\mathrm{14}}}{\mathrm{4}} \\ $$

Question Number 70147 Answers: 1 Comments: 4

Consider the functions f(x)=5×4^(−x) and g(x)=(0.25)^(2x) +4 For what values of x do these functions assume equal values?

$${Consider}\:{the}\:{functions}\: \\ $$$${f}\left({x}\right)=\mathrm{5}×\mathrm{4}^{−{x}} \:{and}\:{g}\left({x}\right)=\left(\mathrm{0}.\mathrm{25}\right)^{\mathrm{2}{x}} +\mathrm{4} \\ $$$${For}\:{what}\:{values}\:{of}\:{x}\:{do}\:{these}\: \\ $$$${functions}\:{assume}\:{equal}\:{values}? \\ $$

Question Number 70145 Answers: 1 Comments: 0

prove that ; arg(z1z2)=arg(z1)+arg(z2). arg(z1/z2)=arg(z1)−arg(z2).

$${prove}\:{that}\:;\:{arg}\left(\boldsymbol{{z}}\mathrm{1}\boldsymbol{{z}}\mathrm{2}\right)={arg}\left({z}\mathrm{1}\right)+{arg}\left({z}\mathrm{2}\right). \\ $$$${arg}\left({z}\mathrm{1}/{z}\mathrm{2}\right)={arg}\left({z}\mathrm{1}\right)−{arg}\left({z}\mathrm{2}\right). \\ $$

Question Number 70138 Answers: 1 Comments: 0

prove that e^(iθ) =e^(i(θ+2kΠ)) given that k=0,±1,±2...

$${prove}\:{that}\:\:\:{e}^{{i}\theta} ={e}^{{i}\left(\theta+\mathrm{2}{k}\Pi\right)} \:\:{given}\:{that}\:{k}=\mathrm{0},\pm\mathrm{1},\pm\mathrm{2}... \\ $$

Question Number 70135 Answers: 0 Comments: 1

sophie−Germain identity a^4 +4b^4 =((a+b)^2 +b^2 )((a−b)^2 +b^2 )

$${sophie}−{Germain}\:{identity} \\ $$$${a}^{\mathrm{4}} +\mathrm{4}{b}^{\mathrm{4}} =\left(\left({a}+{b}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \right)\left(\left({a}−{b}\right)^{\mathrm{2}} +{b}^{\mathrm{2}} \right) \\ $$

Question Number 70132 Answers: 1 Comments: 1

Σ_(n=1) ^(3050) i^n

$$\underset{{n}=\mathrm{1}} {\overset{\mathrm{3050}} {\sum}}\:{i}^{{n}} \\ $$

Question Number 70121 Answers: 1 Comments: 0

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