x] is a O log 2

Q: (Every topo log y is a base for itself) True or false

A:

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: evaluate the Following 'F log p = X and log q=y, x and y. In terms

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: The value of 31 log; v3 is O 0.0 O 15.5 O 31 O 62.0 O 124.0

A:

Q: Show that |Log(2)| < | In |2|| + T.

A:

Q: The domain of definition of Rx) = /log (log x)- log (4- log x)- log 3 is %3D (b) [10°, 10*] (d)…

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: Use the Laws of Logarithms to combine the expressior 5 log(x) 4 ! log(x2 + 1) + 5 log(x – 1) -

A:

Q: What is the zero o of the funcHon Y= loge (x+G)-I?

A: Given: The function, y=logxx+6-1.

Q: (b) Show that u(#) = log log (1 + l#|") belongs to W(U) but does not belong to L(U).

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

Q: Which of the following statements is TRUE? A log log x y log y B log ylog x y c log =lo =-log x D…

A:

Q: Express the following using a single log: 3Log ab2 -Log a2b - 4 Log a/b - 3Log b2

A:

Q: Expand the following expression as much as possible and compute any parts that can be done without a…

A:

Q: The derivate of y = 4 logx? – 5*² is | 8. 8. (2x) 5* In 5 5 x² In 10 x In 10

A: Derivative of the function

Q: 4. Rewrite log(AB²) in terms of logA and logB, or state that this is not possible. log(AB?) = ,

A: We will solve the logarithm problem.

Q: log10y+3log102=5 express y in terms of x

A: Consider the expression  log10y+3log102=5

Q: Find the domain of f(x) = log4(x + 3).

A: We have to find the domain of logarithmic function: fx=log4x+3 We know that for any logarithmic…

Q: Evaluate the integral. 8 r log 4(x + 8) x +8 xp-

A:

Q: Express the given quantity as a single logarithm. - In(x + 2)5 + In x – In(x2 + 3x + 2)²|

A: The exponent 5 becomes the coefficient

Q: Show that if x is positive, then

A: To prove: loge1+1x&gt;11+x

Q: The value of 40 log, V7 is O 80.0 O 160.0 40 O 20.0 O 0.0

A:

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: The domain of log, (x) is

A:

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Make the coefficients into exponent. And they will multiply with the existing exponents.

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: Which of the following is equivalent to 142 = X? O logx(14) = Z O log x(Z) = 14 O log14(Z) = X O…

A: The objective is to find the correct option.

Q: Use the properties of logs to expand: x+5 b) log+ 3x-2 d) log, x(x + 4)

A:

Q: Which of the following statements is not correct? A. log10 10 = 1 B. log (2 + 3) = log (2 x…

A: GivenAlog10 10 = 1B.log (2 + 3) = log (2 x 3)C.log10 1 = 0D.log (1 + 2 + 3) = log 1 + log 2 + log 3

Q: Expand the logarithmic expression In(XY^2Z^3)

A: To expand the logarithmic expressionlnxy2z3

Q: 5) Show the proof that loga M" = r· loga M

A:

Q: 1yn is O(log nº6 O True O False

A: As if Lim (f(x)/g(x))  is finite then we have  f(x)= O(g(x)) So we use this fact

Q: I Find the smallest n so that each of the following functions is 0(x") S(x) = 5x +3x logx +4x +1 is…

A: According to the given information, it is required to find the smallest value of n.…

Q: (ii) Form the PDE by elimınatıng arbitfary log z=a log x+ V1-a' log y+ b

A:

Q: 3 [og,x + logy] – 2[log,a + log, V5]

A:

Q: Given that log z =2, log y = 3 and log z = 4 find log () %3D O 13 O 9 8. O 7 O 11

A: We are asked to find the log

Q: (8) Expand the following into as many logarithms as possible, with what's inside each logarithm as…

A:

Q: Find the integral: log2 X dx In(2)/ 082(x) + C 2

A: Put logx = u then solve it.

Q: Given that log a 2, logy 3 and log z = 4 find log () %3D %3D O 13 8. 7 O11

A: given: we have to find the value of .

Q: what is b if ( log b x) ' = 1/3x

A: Concept: Derivative of log(x) is  logx' logx'=1xln(10)....................(as log is default base…

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

A:

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

A:

Q: State the restriction(s) on the variable x in log(2x-5) – log (4 - x)

A:

Q: (a) f(t) = In(5t - 4) 12 (b) g(x) = log(x² - 25)

A:

Q: Find log,o x: 10a /0.1 10

A:

Q: Prove that A log ƒ (x).= log|1+A7®) f(x)

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: Express

A:

Q: Suppose that A is a number with log(A) = 1.352. What is the value of %3D log(1000A)? *

A: we have to find