Find a so that the graph of f(x) = log ax contains the point (21,2). -.... a = (Simplify your answer. Type an exact answer, using radicals as needed. Use integers o

Q: Express the ratios in as ratios of natural logarithmsand simplify. log2 x/log8 x

A: Given expression is By using base change formula, we have Therefore,

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: 5. Suppose that A = Use the definition of the exponential to calculate exp(At) in terms of familiar…

A:

Q: Find the domain of the function h(x) = log3(x + 6)2.

A: Given function: hx=log3x+62

Q: Use a graphing device to find all solutions of the equation, rounded to two decimal places. x3 - x =…

A: Given x3 - x = log(x + 1)

Q: Find the value of x satisfying log,, (2×+x– 41)=x (1 – log1,5).

A: It is given that, log10(2x+x-41)=x(1-log105)   Here logarithmic properties are going to be useful to…

Q: Use the change of base formula to express log, 8 using In, the natural logarithm. Provide your…

A:

Q: Deduce that log (1 + x) 0. If fix) = log (1 + x), x > 0, uning Maclaurin's theorem, show that for…

A: Given that: fx=log1+x, x>0 To show  log1+x=x−x22+x331+θx3 for 0<θ<1 and log1+x<x−x22+x33…

Q: Solve for x: log (x + 3) + log x = 1. Show that the above equation will have an irrational root if…

A: Solution: To find value of x, log2(x+3)+log2(x)=1log2((x+3)(x))=1   (property of logrithm…

Q: determine the nature of functon for even and odd Ax) = log(x+ Vx² +1) ?+1)

A:

Q: Given that a and b are real and unequal and that logab + logba2 = 3, find a relation between a and b…

A:

Q: Find a so that the graph of f(x) = logax contains the point (2,2) .

A: to find 'a' such that graph of fx=logax contains the point (2,2)

Q: Use the properties of the natural logarithms to simplify the following expressions sin 0 a) In sin e…

A:

Q: Give five examples of exponential functions in the form f(x) = b* and f(x) = a · b° + h with its…

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Q: Find the domain of the function. f(x) = log -6

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Q: The domain for the LOG function does not include which of the following. O 0 negatives O 0 or…

A:

Q: 5. Solve for x without using a calculator: log. (x) + log,(x – 16) = 2

A: The answer is found in step-2

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

A:

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

A: Consider the expression  log10y+3log102=5

Q: Use properties of logarithms with the given approximations to evaluate the exp log 5x 0.699 and log…

A:

Q: Find a formula for the inverse of f(x) = -1+ log2 x.

A: Given function is : fx=-1+log2x To find the formula of the inverse.

Q: 2. a) Express log, 3 in terms of a logarithm to base 3.

A: We have to express

Q: Express the given quantity as a single logarithm. 2)2 In(x 2)7In x - In(x2 +

A: Let the given expression is:

Q: 2. The expression log(3 + x) is undefined for what values of x?

A:

Q: How are the functions ax and log ax defined? Are there any restrictions on a? How is the graph of…

A: Proving that both the functions are defined. Logarithmic functions are the inverse of exponential…

Q: 3) In x-log x = 1. Answer should be in the natural exponential form. %3D

A: This is complicated and lengthy problem, so I can do it in Advanced Mathematics.

Q: Use the properties of natural logarithms to simplify the function. f(x) = = In[ - + In(8) f(x) : %3D

A: By simple using dividation property of logarithm we can solve it.

Q: The domain of log, (x) is

A:

Q: Give five examples of exponential functions in the form f(x)=bx and f(x)= a*bP(x)+h with its domain…

A: we have to give five examples of exponential functions with its domain and range.

Q: What will the coefficient (x – 1)² in the expansion of loge x about x = 1 ? %3D

A: Introduction :

Q: Find the largest value of x that satisfies: log, (22) – log2(x +1) = 2

A:

Q: Find a so that the graph of f(x) = logax contains the point ( 2 , -4)

A: f(x) = logax   Point ( 2 , -4) = (x, f(x)) a = ?   a is positive value.

Q: log, (x17 3 ,17

A: Given expression, log3x17 y173

Q: Find the domain of y = log(3 - 2x). The domain is:

A: The domain is a set of x-values where the function is defined. In other words, the domain is the…

Q: Evaluate loge 7 by Simpson's (i) rd, and (ii) th rules.

A:

Q: Find the domain of the function. f(x) = 3 - 2 log4 (x/2 - 5)

A: Given function is: f(x) = 3 - 2 log4 (x/2 - 5) We have to find the domain of this function.

Q: Find all positive values of 'a' for which the equation log (ax) = 2 log (x + 1) has the unique root.

A:

Q: Let f(x) = logb(3x^2 − 2). For what value of b is f'(1) = 3?

A: Explanation of the solution is given below...

Q: Use the change of base formula to express log, 2 using In, the natural logarithm.

A:

Q: Find a number x such that log3 (5x + 1) = 2

A: We have to find x

Q: Expand the log by using the properties of log.

A: The given log function is,

Q: If p(x)=(x3+2x)^sinx, find p′(x).  Enter an exact answer in terms of a natural logarithm.

A: As the given function :- P(X) = ( X3 + 2X )sinx  P'(X) = ?

Q: If log, 2x + log4(x- 2) = 2 then x is equal to? %3D

A:

Q: 5. Find the domain of f(x) = log(x-4)

A: The given function,   f(x)=logx-4

Q: Solve for X, Show all work A. log(x)+log(x+3)=1 B. 2log(x)+log(2)=log(5x+3)

A:

Q: 2. Find the root Op 3x-logio

A: Given,         3x-log10x-8=0

Q: Find the domain (in interval notation) of the following functions

A: Domain: Domain of a function is the set of values of x for which the function is defined and real.

Q: Express the ratios in as ratios of natural logarithmsand simplify. log9 x/log3 x

A: Consider the provided expression, log9xlog3x Simplify the provided function. Apply the logarithm…

Q: a1- Given the values of x presented in the following table: x 654 658 659 661 If fx) is togu of ()…

A: Given xi 654 658 659 661 According to question given thatf(xi)=log10(xi)Now substitute all of…