27a b² Evaluate log, (- V81cd whenever log, (a) = 4, log3 (b) = 0, log, (c) = -1, and %| log3 (d) = -2. %3D

Q: (1) Determine the largest possible domain, intersection with axes and sign of the function f(x)…

A: To  Determine: The largest possible domain, intersection with axes and sign of the functionGiven: we…

Q: 4 Vrite the domain in interval notation of log. ( ), where c > 0. 2-3x,

A:

Q: Show that -b + VE - 4ac log -b - VE - 4ac + log 2a 2a = log e - log a

A: We have to show that,  log-b+b2-4ac2a+log-b-b2-4ac2a=logc-loga

Q: This Simplification of the expression below, where u, v, and w denote suitable positive realy…

A:

Q: (ii).Given that log, (y-1)+log, = z and log, (y+1)+log, x= z – 1, Show that y = 1+8° and find the…

A: Given: log4y-1+log4x2=zlog2y+1-log2x=z-1 . . . . . (equation 2) Concept: Here we shall use the…

Q: |Example 6.12. Prove with the usual notations, that (i) hD = log (1 + A) = - log (1- V) = siiih- (E)…

A: Please find step by step solution below:

Q: An investment of $49 is earning 7 % - interest per annum compounded annually. If the value, V , of…

A:

Q: 6. Show that the principal branch of the log function can be described by the formula log(z) = S 1/w…

A:

Q: Which of the following represents the domain of h(t)=−log(x)+3?h(t)=-log(x)+3? (0,∞)(0,∞)…

A: We have to find the domain

Q: 16 What is the fully expanded form of log;- .? (A) 2log, 4 -log , 5 (B) 2log;4+-log ; 5 (C) 2log , 4…

A:

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A: To prove,  loga1N=-logaN where, a  and  N are positive real numbers and a≠1. Now, take the left…

Q: 4. If p = a + b + c a. Determine the range of g(x) = e b. If aa = bb = c . -12x-11 ab log.(ab) _ bc…

A:

Q: 11. Find the domain of f(x). a. f(x) = /42-7x. b. f(x) = log3(x - 38) %3D

A: domain= all the values of x for which function exists.

Q: 12. Find r, where log2(ar) – log,(3 – r) = log,(r), and 0 < a < 3. %3D

A:

Q: log,,3 + log, (4x + 1) = log,o (x +1) +1

A:

Q: i3m (a) Find all z such that log:

A:

Q: 2. The function f(x) = log, x is the logarithm function %3D So f(9) = -- f()- with base %3D f(1) =…

A:

Q: Show that loga aMN b = loga M - loga N, where a, M, and N are positive real numbers and a ≠ 1.

A: We have to prove, logaMN=logaM-logaN Let us consider that, M=ax⇒x=logaM          ⋯⋯1N=ay⇒y=logaN…

Q: ´M` Show that loga N log, M – log, N, where a, M,and N

A:

Q: 17. Expand the expression Vx+1(x² - 4) |ninon se log2 183 (r°+27)* -3 081 2

A: Given expression

Q: How do I write the exponential function in the form f(t) = ab^t passing through points (1/2, 4/3)…

A: Given that: The exponential function f(t)=abt passes through 12, 43 and 3, 1283

Q: Exer. 31-32: Find an exponential function of the form f(x) = ba-* + c that has the given horizontal…

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: How do I write the exponential function in the form f(t) = ab^t for the points (-1, 3/2) and (3,…

A: To write the exponential function in the form f(t) = abt

Q: The Gutenberg-Richter Law states that the number, N, of earthquakes per year worldwide of Richter…

A:

Q: 11) 2 log(2)-4log(b)

A:

Q: Show that log,(n) € O(log,(n)) for any b>0 with b 1· Generalize this result.

A:

Q: 7. If log, w = and log6x + log6 y = 1, then determine the value of log7 (4) + log6 (36x²y²) ?|

A: topic- logarithmic equations logaa=1log(ab)=log(a)+log(b)logab=log(a)=log(b)log(am)=mlog(a)

Q: 2 5 Express log b 5.8 m°b in terms of sums and differences of logarithms.

A: The given expression is logbp2q5m5b8.

Q: Log 2 = 0.301, log 3 = 0.477,  log 5 = 0.699 and log 7 = 0.845 Using this information only, find:-…

A: According to the given information, The given log values are:

Q: Show that loga(M/N) = loga M - loga N, where a, M, and N are positive real numbers and a ≠ 1.

A: Here given equation loga(M/N) = loga M - loga N

Q: D.  Express as a single log and natural log :                ( log3 3 +   log3 6 +  log 3 2 ) – (…

A: Consider the given expression: log33+log36+log32-log318 Here, the objective is to express as a…

Q: Q1:-genrate and plot the discrete-time exponential Sequance given by x[n]=(0.8)" u(n)

A: To generate and plot the discrete-time exponential sequence given by xn=0.8nun

Q: Exer. 29-30: Find an exponential function of the form f(x) = ba* that has the given y-intercept and…

A: Given: Find function of the form f(x)=bax 1) the y-intercept is 8, P(3, 1) 2) the y-intercept is 6,…

Q: 9.5. Show that (a). Log(1+ i)? = 2L0((1 + i) but (b). Log(-1+i)² + 2Log(-1+ i). %3D

A:

Q: A. Express in terms of sums and differences of logarithms. 1. log, 6xy®z* 6. log, x³y²z

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Q.2) Fit a second-order Newton's interpolating polynomial to estimate logl0 using log8=0.9030900,…

A: Given that : log8=0.9030900log9=0.9542425log11=1.0413927 The linear interpolation is ,…

Q: x-1 X-n x+n If y = x log show that y, =(- 1)" - 2 (n – 2) ! %3D x+1 (x - 1)" (x + 1)"

A:

Q: 12. Let x be a positive real number and f(x) = log₁0x. Then f(10-x-2) is equal to: I1 f(x) B.…

A:

Q: log(2-j)(3 + jv3)

A: Solve it.

Q: log, (log, (x)) = k

A:

Q: 7. Use log, 2 0.4307 and log, 3 0.6826 to approximate the value of log, 12. O A. 1.5440 O B. 0.8681…

A:

Q: 3. Use log, 2 0.4307 and log, 3 0.6826to approximate the value of log, 54. A. 0.8820 B. 2.4785 C.…

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Q: log, = 3 log, 2– log. (x- 2z) 2 express x in terms of z.

A: Given, logzxz2=3logz2-logzx-2z We have to express x in terms of z.

Q: 2. Which of the following is equivalent to the expression: 2+3 log2 (x + 1) – log (2x – 1)? 2(x+ 1)3…

A: The given expression is: 2+3log2(x+1)-log2(2x-1)

Q: Find a formula for the exponential function f(x) = Ca² passing through the points (2,75) 3 (-1, ³).…

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Q: 6. Find the domain of f(x) = log, [log, [log3(18r – x² – 77)]]

A:

Q: 3-Given that a=log, 3 and b=log ,6, find log, 24 in terms of and b

A: