Show that : log (1+ x) 1+x? dx = log 2 8

Q: (log a)* d.x 1+x²

A: Given ∫0∞logx41+x2dx we can write the above as…

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

A: Given: prove that ddxlogax=1xlna We know that logpq=lnqlnp…

Q: By using u=ln(3x) and dv=6x dx, find ∫ 6x ln(3x) dx. Be sure to include the argument of the…

A: Consider the integral

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: he logarithmic function f(x) = log x is transformed to g(x) = log(x + 1) + 3. Which of the…

A: solution

Q: Given that log x -3 and log y = 5, find log Vy.

A: The given expression is logx2y35 and logx=3   and   logy=5

Q: Evaluate / dx (x+2)²–49 O None to log() x-5 x+3 log() -5 x+7 ts log() x-5 x+9

A: We have to evaluate: ∫dxx+22-49

Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x>0 To show  log1+x=x−x22+x331+θx3 for 0<θ<1 and log1+x<x−x22+x33…

Q: The base of log x is base e true or false?

A:

Q: If log(x + 8) + log(x – 8) = 1 then The value of æ is

A: This is a basic log question that can be solved with logarithmic property. The product rule of…

Q: Find the solution for x: log (Vz+1+1) log V- 40 -3

A:

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

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

Q: Solve the following logarithmic equation:  log x + log(x − 1) = log(4x)

A: Simplify logarithmic equation

Q: If f(x) = 3 log4 (x+2) - 1 and F(g(x)) = g(f(x)) = x, then what is g (x)?

A:

Q: Show that if x is positive, then

A: To prove: loge1+1x>11+x

Q: s (x+1) log(x+1)

A:

Q: d (log4 Vsin x) dx

A: We have to find dlog4sinxdx.

Q: If loga = x and logb-y, then log Vab is equivalent to %3D %3D

A: To find equivalent relation, we will apply basic logarithmic formulas to the given expression.

Q: Prove that : log 2 xp

A:

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

A: we have to rearrange the equation to isolate A

Q: Find the value of Log(-1+i) In/2 + 3ix/4 In5 – in/6 In/2 + ix/4 In/2 – in/3 -

A: We have the formula for principal logarithm

Q: Given that logp q = x 2 and logq p = 1 2x−1 , find x

A:

Q: Suppose we know that log(x) = 6.2. Find the following values. (a) log(10x) (b) log(1000x) (c) logi…

A:

Q: Solve the following equations. log, (2.x – 3) = 3 4 In(3.x) = 8 log x = log(1-x)

A:

Q: Evaluate log2(x²) dx In(2) -log2(x²) + C 4 In(2) log2(x²) + C n(2) (log.(r2))2 (log. (x2))2 1r 4…

A:

Q: What is h′(x) when h(x)=log 7 (8x+4 / x 6 7 x)?

A: Consider the function

Q: First use the appropriate properties of logarrithms to rewrite f(x), and then find f'(x). f(x) = 17x…

A: We have to find f'x and rewrite the function fx using properties of logarithmic: fx=17x+ln17x We…

Q: log (x+8) ) dx 3

A:

Q: Evaluate: dx (x+1) log(x+1)

A:

Q: Deduce the relationship between y and x from the graph shown. log(y) 3.7 0.7 log(x)

A: The general equation of a line in two-point form is: where x and y are variables of horizontal and…

Q: What would be the value of x in log 2 (5x-2) = 3? %D O x = 1

A:

Q: Solve the following equation for X log(x+2) + log(x-1)= 1

A:

Q: a. f(x) = ln 3sqrt(2x^3+5) (Use log properties to simplify first)

A: Solve the following

Q: A Disguised Form of the log Rule, Find

A:

Q: If log(x + 3) + log(x – 3) = 1 then The value of a is

A: considering log base 10   using log property log(a)+ log (b)=log(axb) and  log 10 =1

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

A:

Q: dz Solve dx log (log 2)². z =

A:

Q: The value of x for: log. (e) +4g(9 =x'log(10) is:

A:

Q: Solve the following equation for x:  log(x+1) + log(x+3) = log (x+7)

A:

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: given log y+3 log(x+2): REWRITE as a single log

A:

Q: Solve the following equation for x. log2(12x + 10) = 3 + log2(x + 2)

A: To solve the given equation for x.

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

A: Solution is given below:

Q: b) Find the value of x that satisfies log(x+3)− log x = log x+log 2.

A: Follow the procedure given below.

Q: Given that log x=2.5 and log y = 4 , find the value of log (yx)

A:

Q: Use the Laws of Logarithms to expand the expression. xy (а) log x + 2 (c) log V + 4) (b) In

A: We know that, the property of logarithm is given as logmn=nlogm                 ⋯⋯1logmn=logm+logn…

Q: g(x) = 3 log 2x (0 < x< 10) %3D

A: Here we make the table value and draw the graph...

Q: f(x) = 3x + log(9x − 8), find f(2). f(2) = ?

A: Given a function f(x) , need to find f(2).

Q: If c=log 2, what is log 0.8 in terms of c?

A: