Use definition of hyperbolic function to show that 5e2z 1 2 cosh a + 3 sinhr Hence, solve the equation 4 cosh a+6 sinha = e, leaving your answer in terms %3D of natural logarithms.

Q: r cos? TI Using the properties of the natural logarithmic function, expand In Vr? +1

A:

Q: Q2: Solve the Logarithms Equation. logtan nz (2 + 4 cos ?nx) = 2

A:

Q: Solve the following equation: 7(log; (t)) = log; (t21) Write your answers as decimals rounded to…

A: Answer

Q: 0.30=log(2pi/root g)

A: This problem is related to logarithmic equations.

Q: = (5+ cx*)** y=(5+6x*) (tan(7x)° 312 hint log.differentiat use %3D

A: logab=bloga ddxtan2ax=a sec2 ax

Q: y = 5sec|log, (sin z)]

A:

Q: (x² + 1)? dy if y Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A:

Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

A:

Q: Using properties of logarithms, we can rewrite the equation as In(y) - In(x7 cos(x)), which is…

A: Consider the equation  ln(y)=ln(x7cos(x))

Q: Q2: Solve the Logarithms Equation. n = 3 logtan nx (2 + 4 cos?nx) = 2

A:

Q: Without using your calculator (i.e. show your working), find the value of x: (a) log, 16 = x (b)…

A:

Q: dy Use the properties of logarithms to help perform dx COs x y = ln 3 – 5x2 - dy dx ||

A: As we know that ddxlnx=1x

Q: Disprove the statement log(x + y) = log x + log y by, a) Letting y equal a positive constant of your…

A: Given  The statement log(x + y) = log x + log y

Q: 'x + 2 3. -dx x + 1

A: To integrate: ∫x+2x+1dx Solution: Evaluating the integral.…

Q: By using natural logarithm (ln), find dy/dx for this equation, 384=(x+2)3/4(y+3)1/3.

A:

Q: O Find y'= for each given poblem Sinx b.) y= arc cos 15*) +3 is base of logarithm 一メナ)

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: I need help to find the EXACT solution of the equation below, no decimal approximations please!…

A: To solve the following equation log(2-x)-log(2+x)=2

Q: Determine y′(x) if y(x)=(4x^3+6)^sinx.  Enter an exact answer in terms of a natural logarithm.

A:

Q: State whether the following statement is true or false. Because the domain of ​f(x)=logax is the…

A:

Q: cos e Differentiate y =- using Logarithmic differentitation. nxV2x +1

A:

Q: 1 log(e)= In(10) %3D Use the change of base property to show

A:

Q: Step 1 of 2: Is (9,1) on m(x) log(x + 1) ? %3D

A: Point (9, 1) means i.e. at x = 9  ,   m(9) = 1    Let's see what value we get when we put x = 9 in…

Q: If Ptiq a %3D prove that log ay") a lap + Ba) %3D

A:

Q: Solve for r: log(z + 4) – log(z+3) = 1 You may enter the exact value or round to 4 decimal places

A: Since the question has multiple questions but according to guidelines we will solve the first…

Q: The principal value of tan-' (2i) is :Select one 1 +i-log, 3.a 2 1 loge 3+ i .b c. None of these 1…

A:

Q: Solve for r: log(z) + log(r + 5) 3 1 You may enter the exact value or round to 4 decimal places.

A: We have to solve the logarithmic problem

Q: A Disguised Form of the log Rule, Find

A:

Q: Sind dx/dy if ys log Vitx? 14

A: Given: y=logx1+x2+logx1-x214. So,         dydx=ddxlogx1+x2+logx1-x214…

Q: Find the exact solution to the equation below. (Do not give a decimal approximation.) log(2 – x) –…

A: The solution is:

Q: If p(x)=(x3+2x)^sinx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

A: As the given function :- P(X) = ( X3 + 2X )sinx  P'(X) = ?

Q: Find the positive root of the equation r2 - log10(T) = 12 correct upto 3 decimal places using false…

A:

Q: In arcsin x (V1-x²)arcsin x

A: Given:     ∫lnarcsinx1-x2arcsinxdx    =∫lnarcsinx1-x2arcsinxdx substitute…

Q: Prove the third law of logarithms. [Hint: Start by showingthat both sides of the equation have the…

A: To prove this, we show that the derivative of both sides of the equation is same.

Q: How would you find y' if x^y=y^x using logarithmic differentiation and keeping the answer in terms…

A: Given equation:The given equation is xy = yx.

Q: log2(3x−8)=12   Give your answer for xx in exact form.   Do not use a decimal approximation for xx.

A: Assuming the given equation is:

Q: 3 y = log ( cos DIFFERENTIATE THE GIVEN:

A: The detailed solution is given below Thank you

Q: Determine whether the equation is true or false: log4(2x3) = 3 log4(2x). Where possible, show work…

A: Given information: The log statement, log42x3=3log42x. We have to show the equation is true or false…

Q: 3. (a) Calculate sinh (log(5) – log(4)) exactly, i.e. without using a calculator. Answer:

A: Solution is given below:

Q: Rearrange this equation to isolate A. H = K + log A =

A: Here I am attaching image so that you understand each and every step.

Q: Consider the equation M, = - log10(E) – 10.7 relating the moment magnitude of an earthquake and the…

A: Given - Relation between Moment Magnitude and energy released in a earthquake To find - Factor by…

Q: Solve the Logarithms Equation. logtan nx (2 + 4 cos 2nx) = 2

A: The given logarithms equation is  logtan nx(2 + 4cos2nx) = 2

Q: Evaluate the base (3-4i) logarithm of 10e^2.05i. Express your answer in a rectangular form in 4…

A:

Q: 8. Solve. Give EXACT answers only- (a) e**1 = ! %3D (b) 3log2(x – 1) = 5 – log24

A:

Q: Determine the general solution of (cos x cos y - cot x) dx (sin a sin y) dy, Show your solutions and…

A:

Q: The difference in the noise levels of two sounds is measured in decibels, D, where D = 10 log) (수…

A: This question is based on Substitution of given values.

Q: Please solve the following equations: (a) ln(25(1.05)x)=6 (b) log(1 − x) − log(1 + x)=2

A: Part (a)