9. Find the domain of the logarithmic function f(r) = log(r +3) + log(x² – 6x + 8). Show your work!

Q: Show that the following functions are harmonic in x and y: log√x² + y²

A: Solution

Q: 6. The logarithmic function f(x) = In(x – 1) has the asymptote x %3D

A: Given, Logarithmic function, f(x)=ln(x-1)

Q: Differentiate: f(x) = 2ª + e² + log, 5 f'(x) = 2" In 2+ e² A 1 ® f'(x)= 2" +e² + : 1 © f'(x)= 2" +…

A:

Q: 3. Find syz for ys = In(x + yz) – xcoth-1 log ().

A: Given : Let us consider the given value as,  ys=ln(x+yz)-xcoth-1logzy

Q: 9. What is the maximum value of |Log z| |2| 1? on

A:

Q: Consider the function f (x) = log10 x.   When f (x) is increased by one unit, x must have been…

A: For the function f (x) = log10 x..............................................(1)   When f (x) is…

Q: The logarithmic function f1x2  ln1x  12 has theasymptote x

A: Given f(x)=ln(x-1)

Q: a- Simply the following 1 1. Inx – In(x2 – 1) + 2ln(x + 3) - 2. 5log2 + log3 – log8 b- find x for…

A:

Q: Prove that In x lim I xP for any number p > 0. This shows that the logarithmic function approaches o…

A: Given

Q: snip

A: The exponential function and the logarithmic function is strictly increasing functions for x > 0.…

Q: Determine the maximum and minimum values of the function f(x)= -4 x log2x on the interval [1,4]

A:

Q: Differentiate the function

A: Before we get into solving the question, let's look at the two derivtives shown on the white…

Q: (22x + 2) dx 11 In|x² +4] +2 tan -1 x2 + 4 +C 2 Logarithm function is missing parentheses around its…

A:

Q: d Find (3"). Type In(x) for the natural logarithmic dx function.

A: we have to find the derivative of 3x

Q: 4. Differentiate the function. f(x) = log3 (x In x)

A:

Q: Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value…

A: Given

Q: How is the graph of y =log(x) transform to produce the graph of y=log(2x)+3

A: Given graph of y = log(x), transform it to get the graph for y = log(2x) + 3.Let us first discuss…

Q: at any point h (1, 1) is logx – x

A:

Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: Differentiate the function with respect to x f(x) = 2* · log37*²-4

A: If hx and gx are two differentiable function and fx=hxgx Then f'x=gx×ddxhx+hx×ddxgx

Q: 54. For any positive constant k, the derivative of In (kx) is 1/x. Prove this fact (a) by using the…

A: Given for any positive constant k, the derivative of ln (kx) is 1/x. To prove that  a) by using the…

Q: - Use the fact that d In x/dx = 1/x, as well as the change-of-base theorem for logarithms, to prove…

A: Given : d lnxdx = 1x d logaxdx = 1xlna

Q: Sketch on graph a) y = 2x-3+ 3  b) y = log2 (x – 4)

A: a)

Q: a) Express the new function h(x) = log2(x + 2) in terms of the original function f (X) = log2(x).…

A:

Q: Prove that In x lim xP for any number p > 0. This shows that the logarithmic function approaches…

A: Prove that limn→∞ ln xxP=0for any numbers P>0

Q: 22. Suppose f(x) = log x + log(x – 3). Find the x-value for which f(x) = 1.

A:

Q: O f (x) = – log(x – 2) - -

A: Given: The functions, f(x) =12x - 2f(x) = log2 ( x +2)f(x) = - log ( x -2)f(x) = ln x + 2 f(x) =…

Q: (b) Show that u(2) = log log (1 + la|") belongs to W12(U) but does not belong to L (U).

A: Given: u(x)= log log(1+|x|^-1)

Q: When comparing the f(x) = x² + 2x and g(x) = log(2x + 1), on which interval are both functions…

A: Let's find interval when both functions are negative.

Q: Find the equation of the curve y=g(x)=ax+b, which osculates with the graph of the logarithmic…

A:

Q: II. Determine the derivative of the ff. logarithmic functions 1. y = 25 In 5x 2. y = -10 In 3x4 3. у…

A:

Q: Find the linearization of the natural logarithm f(x)=lnx at x=1.

A:

Q: 4. Which of the following functions grow faster than x2 as x→∞? Which grow at the same rate as x²?…

A:

Q: 2. Compute for the value of x in a given logarithmic inequalities loga(x+1) > log:(x2). a. x > ½ b.…

A:

Q: FInd the Domain of these functions. f(x) = log7 (4x + 8) f(x) = ln(4x − 20)

A:

Q: 2 Show that the following functions are harmonic in x and y: 2 log√x² + y²

A:

Q: - f(x) = - f(x) = x-2 g(x) = 5 In x - 2* g(x) = 4x' log, x %3D f(x) = 10* · e*

A: Solution of question is written in below steps.

Q: Find Y for the following function: dx 3- y = log,(x3- x) 4- y = In 5- tan-1 V4x – 5

A: we have to find the derivative of the following

Q: Determine the maximum and minimum values of the function f(x)=-4 •log 2x on the interval [1,4]

A: Given function is  on interval [1, 4].

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: 5. Find y' and y". In x (1) f(x)= (2) f(x)= log,o * 6. Find y' if y=In(x²+y?)

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the domain of the function. x+4 h(x) = log ɛ %3D

A: We have to find the domain of the function h(x) = log8x+4x.

Q: 36. Determine the x-intercept(s) of f(x)log2(3x-4)1

A: Rules:x intercept(s): is (are) the point(s) where the graph crosses the x-axis. In order to find the…

Q: 5. Prove if the following function is differentiable y = x loge-*

A: Given that: y=xloge-x

Q: 3) For f(x) = log2 x and (x)=√x-4, what is the domain of f(g(x)) and g(f(x))?

A: The function f(x)=logx is defined for x>0 The function f(x)=x is defined for x≥0 Note: If logba=c…

Q: 1. Find for the following functions : dx 2x (ans.: 3x' log,( 3 – 2x)-’ (3–2x )In 2 45) y=x' log,(3–…

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.