Ex 96, 7 For each of the differential equation given in Exercises 1 to 12, find the general solution 𝑥𝑙𝑜𝑔𝑥 𝑑𝑦/𝑑𝑥𝑦=2/𝑥 𝑙𝑜𝑔𝑥 Step 1 Put in form 𝑑𝑦/𝑑𝑥 Py = Q xlog x 𝑑𝑦/𝑑𝑥 y = 2/𝑥 log x Dividing by x log x, 𝑑𝑦/𝑑𝑥𝑦" × " 1/(𝑥 log𝑥 ) = 2/𝑥 𝑙𝑜𝑔 𝑥" × " 1/(𝑥 log𝑥 ) 𝑑𝑦 Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeThis problem has been solved!
If Log Xy 3 1 2 Logx Logy Then Find The Value Of X Yy X
If log(x y/2)=1/2(logx logy) prove that x=y
If log(x y/2)=1/2(logx logy) prove that x=y-See the answer A) If log (xy/3) = 1/2 (logx logy), show that x^2 y^2 = 11xy B) Show that sin^2x cos^2x = 1 for pi/3Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and more
Log Properties
Get answer If x^2y^2=27xy, then show that log((xy),(5))=1,2logxlogyIf $x > y$, can you prove $x \ \log y > y \log x$, where $x \ge 1$ and $y \ge 1$ I encountered this problem in a paper I read and somehow cannot prove itSolve for x log of x=y log(x) = y log ( x) = y Rewrite log(x) = y log ( x) = y in exponential form using the definition of a logarithm If x x and b b are positive real numbers and b b ≠ ≠ 1 1, then logb (x) = y log b ( x) = y is equivalent to by = x b y = x 10y = x 10 y = x Rewrite the equation as x = 10y x
Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack ExchangeBy default, mathlog \ x/math would have a base of 10, so mathx = 10^y/math In general, in the equation mathy = log_b \ x/math, where b is the base, mathx = b^y/math If x = e^cos2t and y = e^sin2t , prove that dy/dx = ylogx/xlogy asked in Limit, continuity and differentiability by Raghab ( 504k points) differentiation
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals For math, science, nutrition, history Prove #x^(log_10(y)log_10(z))y^(log_10(z)log_10(x))z^(log_10(x)log_10(y))=1# Use the base 10 logarithm on both sides #log_10(x^(log_10(y)log_10(z))y^(log_10(zGet answer If x^(y)=e^(xy), prove that (dy),(dx)=(logx),((1logx)^(2))
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Here we have to use implicit differentiation As log(xy) = x2 y2 or logx logy = x2 y2 assuming base is e, we have on differentiation 1 x 1 y dy dx = 2x 2y dy dx or dy dx (2y − 1 y) = 1 x −2x or dy dx = 1 x −2x 2y − 1 y = y − 2x2y 2xy2 −x In case base is 10, we can write it as lnx ln10 lny ln10 = x2 y2X^2 y^2 = 23xy => x^2 y^2 2xy = 25xy => ( x y )^2 = 25xy => x y = 5 (xy)^1/2 So , taking log both sides , /5 = 1/2 ( logxy) log(xy)/5 = 1/2(logx logy ) Hence$\begingroup$ I figured if I multiplied both sides by 5 $2^y5 = 4^x5$ I would have $10^y = ^x$, then $\log y = ^x$ as you can see that didn't actually help me $\endgroup$ –
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The equation 2 lo g 2 (lo g 2 x) lo g 1 / 2 lo g 2 (2 2 x ) = 1 has View solution If lo g 2 = 0 3 0 1 0 and lo g 3 = 0 4 7 7 1 , then the value of lo g 2 4 will beradg8 and 125 more users found this answer helpful If yx = eyx, then prove that \(\frac{dy}{dx}=\frac{(1log\,y)^2}{log\,y}\) Consider the function y = x^x √x 1Express the above function as logy = (x 1/2)logx 2
Log Properties
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X square y square=23xy,prove that log xy/5=1/2(log xlog y) Get the answers you need, now! If xy = ex y, then prove that dy/dx = (log x)/(1 log x)2 Welcome to Sarthaks eConnect A unique platform where students can interact with teachers/experts/students to get solutions to their queriesLog{{xy}/3}=1/2{logxlog Y} log(xy) log(3) = 1/2(log xy) log(xy) log(2) = 1/2(log xy) 2xy 4 = xy xy = 4 now x/y y
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You can put this solution on YOUR website!Get answer If x^2y^2=7xy, then prove that log((xy),(3))=1,2(logxlogy)Stack Exchange network consists of 177 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers Visit Stack Exchange
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Click here👆to get an answer to your question ️ If y^x = e^y x then prove that dy/dx = (1 logy )^2/logy Join / Login > 12th > Maths > Continuity and Differentiability > Logarithmic Differentiation (d x d y ) 2 − x yLet's change the first equation to single log terms with no coefficients math 2\log(xy) = \log((xy)^2) = \log(x^22xyy^2) /math math \log(5) \log(xI suppose you understand that to solve you must have an equation that is an equal to sign If you ask how to solve logx/logy it makes little sense to me But then maybe you intend to inquire about the Logarithmic Identity Which I state here with
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Solve your math problems using our free math solver with stepbystep solutions Our math solver supports basic math, prealgebra, algebra, trigonometry, calculus and moreClick here👆to get an answer to your question ️ If xy log(x y) = 1, prove that dydx = y(x^2y x y)x(xy^2xy)Ch 1 Real Numbers, Exercise 155 If x^2 y^2 = 25xy, then prove that 2log(xy) = 3log3 log xlogyAP SCERT Mathematics Textbook, Pg 23CCE MODEL, AP/TG Cl
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4 log x y =logx−logy ProofToprove(1),fixyandcompute d dx logxy= 1 xy d dx (xy)= 1 xy y= 1 x = d dx logx x→0 logx=lim n→∞ log 1 2n 1exy=exey 2e−x= 1 ex 3 (ex)r=exr forrationalr ProofThisisleftasExercise4If you like this video then dont forget to subscribe to my channel for more videos if x^2y^2=10xy prove that 2log (xy)=logxlogy3log2 How to solve if x^2y^2=10xy prove that 2log (xy)=logxlogy3log2 I have a maths problem to solve, can anyone drop a paper solution for if x^2y^2=10xy prove that 2log (xy)=logxlogy3log2 Add a video to describe the problem better
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Singhsaurav5600 Incredible29 Incredible29 Heya user Here is your answer !!To ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If `x^2 y^2 = 14xy and 2log (k (x y))=(logxlogy)`, then the value of k isRewrite in Exponential Form log of x=1/2 log(x) = 1 2 log ( x) = 1 2 For logarithmic equations, logb(x) = y log b ( x) = y is equivalent to by = x b y = x such that x > 0 x > 0, b > 0 b > 0, and b ≠ 1 b ≠ 1 In this case, b = 10 b = 10, x = x x = x, and y = 1 2 y = 1 2 b = 10 b = 10 x = x x = x
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Techniques Of Differentiation Further
The point of intersection is (10, 1/10), assuming the logarithms are in base 10 Isolate the logx in equation 1 logx = 2 logy Substitute for logx in equation 2 2 logy logy = 0 2 2logy = 0 2(1 logy) = 0 logy = 1 y = 10^1 y = 1/10 logx = 2 log(1/10) logx log(1/10) = 2 log(x/(1/10)) = 2 10x = 10^2 10x = 100 x = 10 The solution point is (10, 1/10) Hopefully this helps! If y = (sin x) x sin1 (x) 1/2, find dy/dx Mention each and every step find dy/dx y = (log x) x (x) log x mention each and every formula and minute details find dy/dx mention each and every formula and minute steps and detail Y = x x e (2x 5) Differentiate x sinx w r to x Differentiate (log x) cot x w r to xTo ask Unlimited Maths doubts download Doubtnut from https//googl/9WZjCW If log x logy log z = (yz) (zx) (xy), then
Partial Differentiation
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log (xy)/2 = 1/2 ( logx logy) log (xy) / 2 = 1/2logxy xy/2 = √xy xy = 2√xy Squaring on both sides; logx logy = 6 logx logy = 2 Now just solve as usual for logx and logy Then raise whatever base you are using (probably 10) to the respective powers 👍X²y²2xy =4xy x²y² = 6xy Hence proved !
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If x = e^cos2t and y = e^sin2t , prove that dy/dx = ylogx/xlogy asked in Limit, continuity and differentiability by Raghab ( 505k points) differentiationSimplify/Condense 1/2* log of x log of y log of z 1 2 ⋅ log(x) − log(y) log(z) 1 2 ⋅ log ( x) log ( y) log ( z) Simplify 1 2log(x) 1 2 log ( x) by moving 1 2 1 2 inside the logarithm log(x1 2) −log(y)log(z) log ( x 1 2) log ( y) log ( z) Use the quotient property of logarithms, logb (x)−logb(y) = logb( x y) log b ( xTrue, if you can calculate the discrete logarithm, then it would be easy But that's hard too, eg see Wikipedia for more details No series in y can yield x To see this, first note that, replacing y (x) by y (x)a_0, one can assume without loss of generality that a_0=0 Introduce the series A (u)=\sum\limits_ {n=0}^ {\infty}a_nu^n
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$\log{\Big(\dfrac{xy}{3}\Big)}$ $\,=\,$ $\dfrac{1}{2}(\log{x}\log{y})$ The left hand side expression is purely in logarithmic form but the right hand side expression is also in logarithmic form but the factor $\dfrac{1}{2}$ pulled us back in eliminating the logarithmic form from the equation
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