What is the Domain of the following logarithmic functions? 1) f(x) = log(3x - 21) 2) f(x) = log(2x + 16) 3) f(x) = log2 (x - 2)

Q: Solve for x using sci notation x=log(y^5) ; if (log y) = 1.2 x 10^-4

A: We have to find value of x by using scientific notation.

Q: 5. Solve for x using log properties: log3 (x) + log3(2x – 3) = 2 |

A: Consider the given logarithmic equation, log3x+log32x-3=2 use the logarithmic property,…

Q: 9. What is the maximum value of |Log z| |2| 1? on

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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: If the base  b of the exponential function is a real number between zero and 1  (0 < b < 1 ) , then…

A: Exponential functions have the form f(x) = bx, where b &gt; 0 and b ≠ 1. Just as in any exponential…

Q: 14. For the logarithmic function (x)=log, (x-4), explain why x=0 is not in its domain.

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Q: How does ƒ(x) = logx (2) compare with g(x) = log2 (x)? Here is one way to find out. a. Use the…

A: We need to plot the two logarithmic functions :

Q: 5. Show that --I+#^) log, (V +1- x) + log, (VF+1+x) = 0 x². x² + 1 + x

A: We know the property of logarithm, logb(a)+logb(c)=logb(ac)

Q: 7. f(x) = 6e* + log2(7x² + 3x + 1) f'(x) =

A: Given: fx=6ex+log27x2+3x+1 Differentiating fx with respect to x, f'x=ddx6ex+log27x2+3x+1…

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: If x2 + y2 = 25xy . Then prove that 2 log(x+y) = 3log3 +logx + logy

A: It is given that x2+y2=25xy add 2xy to both sides  x2+y2+2xy=25xy+2xy using the formula…

Q: domain of the logarithmic function f(x)= logax is

A: The domain of the logarithmic function f(x)= logax is given by

Q: A manufacturing company finds that the number of products they can manufacture, X, is related to the…

A: First, we have to calculate the profit from the profit function P, then we can calculate the profit…

Q: 17. log (x² + 3) - log(x + 6)

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Q: 1 [log, (x- y) - log; (x+ y)]

A: Given that: 12log5(x2-y2)-log5(x+y)

Q: 4. Find the domain of the log function. y = In((7 – x)(x + 10)) Use a sign chart.

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Q: 4. Differentiate the function. f(x) = log3 (x In x)

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Q: #11

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Q: 1 (log, x)' 3x ise b =?

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Q: Show that loga(√x + √(x - 1)) + loga (√x - √(x - 1) = 0.

A: To show: That logax+x-1+logax-x-1=0. Concept used: Logarithmic product rule: logax·y=logax+logay…

Q: x² 6 + ,X log (x² + 7)(x³ – 5)² -

A: Laws of Logarithm:

Q: Differentiate the function with respect to x f(x) = 2* · log37*²-4

A: If hx and gx are two differentiable function and fx=hxgx Then f'x=gx×ddxhx+hx×ddxgx

Q: Does the function f(x)= logarithm x with the base of 1/2 approach a certain real number as the value…

A: To Discuss: a. Does fx=logarithm x, with base 12 approaches a certain real as xincrease positively?…

Q: Express in terms of logarithms of x, y, z, or w.

A: The given expression is log3xzy

Q: 2. Express as a single logarithm 4 log, x² + 3 log, ) – log, x X 5

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Q: Find all x- and y-intercepts of graph of y = −3+log2 (x2-x+2)

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Q: 2. Evaluate [log(-1-1)(-2-j2)] tan(4 + 3i) cosh-

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Q: Express in terms of logarithms of x, y, z, or w.

A: The given expression is logax3wy2z4

Q: Does the function f(x)- logarithm of x with the base of 4 approach a certain real number as the…

A: Consider the given function as fx=log4x.

Q: (a) Use the definitions of hyperbolic functions in terms of exponentials to prove that 8 cosh'x cosh…

A: a) LHS =  8cosh4x  =  8(cosh2x)2  =  8 * ((1/2)( cosh(2x) + 1))2  =  2 (cosh2(2x) + 2cosh(2x) + 1)…

Q: Show that loga (x + √(x2 - 1) + loga (x - √(x2 - 1) = 0.

A: To prove: logax+x2-1+logax-x2-1=0

Q: How is the logarithmic function (x) = log2(x) related to the exponential function g(x) = 2×? The…

A: Given, fx = log2x gx = 2x

Q: 4. The expression log(sinx) – log(cos.x) , 0<x<, is equal to A. log(sin x cos x)

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Q: Find all x- and y-intercepts of graph of y = -3 +log2(x2 - x +2).

A: Given function is y=-3+log2x2-x+2

Q: For each part of this question, you may (but are not required to) use any of the following facts. •…

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Q: How does the second to last step come about? How does "log(5^x/2) + log(5^1/2)" turn into "log (sq.…

A: Note: From seeing the previous explanation we observe that there is a typing error in the second…

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: Which grows faster In(x) or log (x)

A: ln(x) grows faster than log(x) Look for the graph using Desmos graphing calculator.

Q: Differentiate the following logarithmic functions and show that y=ln(x+5)2≠[ln(x+5)]2

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Q: Why is  the logarithmic function  not defined for negative values of x, thesoftware can produce only…

A: The definition of logarithmic function is, logbx=y⇒by=x The output value of exponential function by…

Q: 5. The natural logarithmic function f(x) In x has the %3D asymptote x %3D

A: Given function - f(x) = ln(x)

Q: function

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Q: Just as exponential functions are distinguished by their rapid rate of increase, the logarithm…

A: Consider the graph:

Q: 1.Solve by logarithmic differentiation (x+1)(x+2)(x+3)2 Y=In( V(x+3)3(x+4)4

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Q: d Find (2"). Type In(x) for the natural logartihtm dx function.

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Q: 2. Evaluate [log(-1-/)(-2- j2)] tan(4 + 3i) cosh-1

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Q: 3. log (x²+x)-log.(x-1)-2 А. 2 Oi J. оо о で В. 16 C..X D. - 16 -

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…