Find and simplify whenever possible. dx y = log10(x² + 1)² ||

Q: (log a)* d.x 1+x²

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

Q: dy (x² + 1)? if y = 2) Find dx (x² – 1)³ a) without the aid of logarithmic properties b) using…

A: Here we have to find the the derivative of y

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

A:

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

A:

Q: d (4 log4(x) + 13) dx Find

A: Given, ddx4log4x+13  We have to find the derivative.

Q: If loga = logx – 2(logy + logz), then a is equal to O Ax-y²z? В. Х v²z? O C.x-2y+2z OD. X 2y +2z

A: given,

Q: s) Use the properties of logarithms to find dx y = In 4] sin' (3x) 5* √√x² +1

A: We can solve the derivative of 'y' as below.

Q: y = log( 2x'Vx² -1) 8.

A:

Q: 2. y = loga(x³ + 2x – 2)

A:

Q: Find the domain of y = log(2 – lx). The domain is:

A:

Q: Express the given quantity as a single logarithm 1/7 ln(x + 2)7+1/2[ln(x)-ln(x2+3x+2)2]

A: Formula used:

Q: 1 3 log, (x²) + log, vx

A:

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

A:

Q: d (log4 Vsin x) dx

A: We have to find dlog4sinxdx.

Q: Condense the into a following (b) Single logarithm. 2 In (x+1) +3 InCy)-Ź Incx)

A: Condensing the expression to a single logarithmic value

Q: y = log₂ (1+x²)

A:

Q: y=log33/x+3/x

A:

Q: Solve the following equation for x: log3(ln(x)) = 2.

A:

Q: y=x^logv5(x) dy/dx=?

A:

Q: Find the solution of the equation, correct to two decimal places. log2(x+2) + log2(x−1)= 2

A: We gonna use log properties to sole this problem log m + log n = log mn  loga x = y  => x = ay

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: y = log, (2a – 1) · (x³ – 4x)

A: Given: y=log42x-1·x3-4x Formula used: Product rule: f·g'=f'·g+f·g' Constant multiple rules of…

Q: solve the following equation log2 (5Vx – 5) + log2(v – 1) = 3

A:

Q: r(x) = 5 log4 (3x + 10)

A:

Q: (а) е" =D1 %3D (b) log(x – 3) + log(x - 6) =

A: Given that: (a)ex2-9=1(b)log(x-3)+log(x-6)=1

Q: 2. 2 log x – 1 = log(x-1)

A:

Q: log (x³y¹z) = b

A:

Q: In2 log2x dx

A:

Q: Solve the following logarithmic equation. log(2x - 2)= log(x + 1) + log(4)

A: Given: log2x-2=logx+1+log4 Now by using the logarithmic property, loga+logb=loga·b…

Q: d -log(z) = dz (Z

A:

Q: b. (3e* C. z? – 2z = log(-2), Calculate the value/s of z

A:

Q: dz Solve dx log (log 2)². z =

A:

Q: 10 y =x X log. Cax+1) logon Do

A:

Q: d (3 log6(x) + 20) dx Find

A:

Q: dx Express your answer in logarithmic form. x2 + ax

A: ∫dxx2+ax

Q: f (x) = ex ln(5x) - ex^3 +2 + log(e2x^2), find f '(3)

A: The given expression is f(x)=exln(5x)-ex3+2+log(e2x2).

Q: Find the value(s) of x for which the equation is true. log(x + 2) = log(x) + log(2) X =

A:

Q: Solve the following logarithmic equation:  log2(x − 2) + log2(x + 1) = 2

A: Given,

Q: d -log(z) = dz z O O 2- 1

A: We need to differentiate the function log(z) with respect to z. Differentiation is the process of…

Q: 00 dx 2- So V- log x

A:

Q: condense: log d + z log q

A: Here given that  logd+ zlogq  we know that.    alog(b) = log(b)^a

Q: Find dy dx given (х* + 3x — 1)° /1 – 3x³ y , by using property of logarithms.

A:

Q: Solve the equation for x .   a) ln( x + 1) + ln( x - 1) = 1  b) log5(c x)= d

A: Part (a) - lnx+1+lnx-1 = 1lnx+1x-1 = 1                                  lnab = lna+lnblnx2-1 = 1…

Q: dx x log10X

A: Let's find.