1. Combine log, (x – /24) + log, (x + /24) into one logarithm. 2. Solve the equation log, (x – /24) + log, (x + v24) = log,(2x). Exact answers. If there are more than one solution, seperate each solution with a comma. If there is no solution, write DNE.

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: Express the following logarithms in terms of ln 2 and ln 3.c. ln (1/2)           d. ln( 9)^1/3

A: Given: c  ln12  d ln913 Formula Used: 1 lnmn=lnm-lnn2 lnxn=nlnx

Q: Given that ln(5) = x and ln(7) = y, express the given logarithmic value in terms of x and y.…

A: Given that ln(5) = x and ln(7) = y. Use the property of the ln function

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

A:

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

A:

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: Solve the following equations for x (a) 31-x - 92x (b) log2(z – 2) + logą z = 3

A: On solving the first

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

A: logab=bloga ddxtan2ax=a sec2 ax

Q: 1. Which of the following is equivalent to y= log, x ? (1) y = x' (3) x= 7" (2) x = y' (4) y = x%

A:

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

A:

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

A:

Q: Differentiate g (†) = 4 log, ( t ) – In ( t )

A: Given g(t)= 4log3(t)-ln(t) Now we have to differentiate g(t) as shown below

Q: 5. Find y' and y". f(x)= log,0 x Find y' if y=In(x²+y?) 6.

A: f(x) = log10x ∴ f'(x) = 1/x and f"(x) = -(1/x2)

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

A:

Q: 17. Without using a calculator, solve each of the following: |4*+3 V 16* log, (x+3)+ log, (x-3)=2 b.…

A:

Q: 2. Given that x> 0, the value of x for which log, x + log,(6x + 1'0) = 1 is D

A:

Q: 1) Solve for x and y in the following simultaneous equations *a) log, x = 2; 5y= x +12 log, y *b)…

A: We have to solve for x and y in the following simultaneous equations.

Q: 9⋅7x=3.5e^(2x) Find x using natural log

A: Given exponential equation is:Solve for x using natural log.

Q: 6. If 16 and log,(x – y) = 2, calculate the values of x and y algebraically. 1/2

A: Given,12x+y=16and log8x-y=2

Q: Which of the following functions grow faster than In x as xoo? Which grow at the same rate as In x?…

A:

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

A:

Q: If logy =c- log,x, where y> 0 andx > 0, then y is equal to A. c-X В. 3 D. C.

A: To solve the given logarithm

Q: woubnat Solve for x 7* = 12 a. b. log(x+5)+log(x-4)=1 c. log, (x+3)-log, x= log, 7 %3D d.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Solve for x. log, (x+7)=3– log, (x+ 5) If there is more than one solution, separate them with…

A: To find the value of x for the expression, log2x+7=3-log2x+5

Q: 0:A-If y = 2cc (20) and x = etot(20), Prove that: - (answer one only) dy *- (In2).. log, x %3D dr B-…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Express the following logarithms in terms of ln 2 and ln 3. ln √13.5

A: Express ln13.5 in terms of ln2 and ln3.

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y – 3 loga x 6.…

A: This is a problem related to logarithm properties. Based on the general formula we can answer the…

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

A:

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

A: we have to rearrange the equation to isolate A

Q: 2 log , x + 12log, y

A:

Q: given that ln 2 = x, ln 3 = y, and ln 5 = z, express each of the given logarithmic values in terms…

A: Given:   ln 2=x , ln 3=y, ln 5=z   To find:   The logarithmic values in ln 30 in terms of x, y, z…

Q: (a) Solve the following: 1 (i) 2-6 8. (ii) log, (x+3) =1– log,(x–1)

A:

Q: B. Convert to an exponential equation. 1. log, T =x 2. t= log, 7 3. In 0.38 =- 0.9676 5. log 0.01 =-…

A:

Q: Given 2 log3(x + y) = 2 + log3x + log3 y, show that x² + y² = 7xy.

A:

Q: Express the following logarithms in terms of ln 5 and ln 7. ln 9.8

A: The given expression is ln 9.8

Q: 4. Solve the following logarithmic equations: a) logx+log(x+15) =2 b) log,(x+1)= 1 +log, x d)…

A: We have to find value of x for given problem

Q: Q3. (i) Solve for x: a. 32x = 22x-4 b. Vlog2(x – 8) + log2(x + 8) = 64 %3D

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: log, x + log, y+ 6log, -

A: Using Rule's of Logarithm

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: 19. f(x) = log,(7)* 20. f(x) = xlog101000 %3D

A:

Q: B. Express as a single logarithm and, if possible, simplify. 1. log, x + 4 loga y - 3 log, x 6.…

A: According to our company's guidelines I can only answer first three subparts of the question B since…

Q: b) Given that log, (y-1)+log,|| |= z and log, (y+1)+log, x = z-1, Show that y? =1+8² and find the…

A:

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

A:

Q: 2 log, 64|,B = |** 6 [x +3 = 4 В 10 -4] 4 [m LetA = 4 21 3. 2 -7 5 4 and D =, *,. Find X, if AB" +…

A: To find the value of X.

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

A:

Q: t(z)= 2z log2z  , t '(z)?

A: