Determine whether the statement makes sense or does not make sense, and explain your reasoning : "I expanded log4 √(x/y) by writing the radical using a rational exponent and then applying the quotient rule, obtaining 1/2log4 x - log4 y."

Q: 1 Give one example r that makes log. (r) rational but not an integer

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Q: Simplify the expressions below. - In 10 (b) log - {x² - 9) (c) log 285x-3 (a) -

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Q: Recall that Log corresponds to the principal argument. What is the real part of Log(-3+3i)? What is…

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Q: Find the inverse 2-Transforrm of log(z f log 241 by Power senies method and by division method

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Q: Use the product rule for logarithms to find all x-values such that log12(2x + 4) + log12(x + 3) = 2.…

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Q: (a) Exactly calculate 2log4 8 Tog, 2 (b) Write In (/2.x + 1) + In(æ) – In(|sin æ|) in one…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: How is log 763 written in terms of natural logarithms using the change-of-base theorem? The formula…

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Q: Because I cannot simplify the expression bm + bn by adding exponents, there is no property for the…

A: The expression bm+bn cannot be simplified by adding exponents, because we add the exponents when we…

Q: Simplify by writing as a single logarithm: Show all steps clearly including use of 'logʻ rules.…

A: Given, log(2x²+7x+6)-log(x²-4)

Q: Recall that Log corresponds to the principal argument. What is the real part of Log(-3+3i)*? What is…

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Q: 2. Simplify by writing as a single logarithm: Show all steps clearly including use of 'log' rules.…

A: topic - logarithmic

Q: Express as a sum or difference of logarithms without exponents. 8 log c What is the equivalent sum…

A: Topic = Algebra

Q: Vx*+12 In (x+16)/x-3

A: Given,                   lnx4+123x+16x-3=?

Q: Combine the following into one single logarithm with a coefficient of 1 in front of the entire…

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Q: Use the change-of-base formula to find the approximate value. log16 x5 = log64 125 - log4 √x

A: The change of base formula, from base b to base a, is:   logb(x)= loga(x)loga(b)log16x5=log 16log x5…

Q: Use the laws of logarithms to expand and simplify the expression. x3 In Vx (1+x)5,

A: To simplify the expression

Q: Express in logarithmic form for the base. ab= N

A: Given, ab=N Aim: express in logarithmic form

Q: Recall that Log corresponds to the principal argument. What is the real part of Log(-4 + 4i)? What…

A: Principal argument lies between (-π  π]

Q: Change the logarithmic statement to an equivalent statement involving an exponent. log2 6 = x

A: The exponent of a number says how many times to use the number in a multiplication and the logarithm…

Q: Expand the given logarithm and simplify. Assume when necessary that all quantities represent…

A: Consider the expression,

Q: Use the laws of logarithms to expand and simplify the expression. In Vx (1+x)5,

A: We have to express the expression

Q: Check the result by using the related exponential form.

A: As you asked only question (3) so , I answered here only for subpart (c)

Q: Simplify the expression log(2x – 2) – log(x² – 1). State the restrictions on x. - -

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Q: ense the expression below into a single thm. 133.16 log 64 +log (x+5)

A: Topic:- Algebra

Q: The change-of-base formula states that logb x can be written as a ratio of logarithms with base a as…

A: Change of base formula:

Q: The correct expresssion for log is.. . x+8

A: Given the expression is log x4x+8 To simplify the given expression:-

Q: I estimate that log8 16 lies between 1 and 2 because 81 = 8 and 82 = 64.Determine whether the…

A: Given information: The value of log816 lies between 1 and 2, because 81 = 8 and 82 = 64.

Q: The change-of-base formula states that log, x can be written as a ratio of logarithms with base a as…

A: We have to change the base of the given logarithm  we have,  logbx

Q: What is the domain of ƒ1x2= logb x2? What is the range of ƒ1x2= logb x2?

A: Given: fx=logbx2 we know that domain of logx is x greater than zero similarly, domain of given…

Q: Use the power rule to expand the logarithmic expression: log (4x)5.

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Q: log(x) is the exponent to which the base 10 must be raised to get ---Select--- v So we can complete…

A: See below

Q: t is known that log4x = k. Given this information, write the expression log4(64x^5) in terms of k

A: Given that log4x=k. The main objective is to calculate the value of the expression log464x5. The sum…

Q: Express in terms of sums and differences of logarithms. 168 4 m log c c'a 16.8 4 m log c 7.3 са…

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Q: Use the One-to-One property to solve for x: log, (x + 2x) = log, (3x + 2).

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Q: 2. log(3+j7)[ln(7+j3)]

A: Given - log3 + j7ln7 + j3 To find - Evaluate the given expression and write in rectangular form.

Q: Expand the logarithimic expression.

A: Given: y=lnx2-1x2+1 We know that lnmn=nlnm…

Q: convert the exponetial in logaritham form. 4v=a

A: logarithmic form will be  log4a = v

Q: Use the change-of-base formula to find the approximate value. log4 x3 + log2 √x = 8

A: The logarithmic equation is: log4 x3 + log2 √x = 8 We have to solve this equation. We have, log4…

Q: The expansion of the logarithmic expression x² (x+1) In (2x-3) is

A: The given logarithmic expression is lnx2x+12x-3. The following formula are used in solving the given…

Q: 1. Write the logarithm log [2x(x²+3)*| as a sum or difference of logarithms. Expand and V4-3x…

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Q: Determine whether the statement makes sense or does not make sense, and explain your reasoning.

A: Given- log4xy To find- Whether the expanded form of the above expression is 12log4x-log4y correct or…

Q: Use the definition (p. 75) and properties of logarithmic functions (Theorem 1, p. 77) to solve the…

A: We need to find value of x.

Q: Use the properties of logarithms to write lnx√x/x−1 as a sum or difference of simple logarrithmic…

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Q: Expand the logarithimic expression.

A: lnx4+123x+16x-3

Q: When writing the original expression in terms of simpler logarithmic expressions, an error was made.…

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Q: Solve for the inverse fonction of flA)= log (4)- domain and range of both f and f

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Q: Use your knowledge of the logarithm properties to expand In (x – 1)(2x + 1)6 x²-9 as a sum or…

A: Given: logarithmic properties are :

Q: Simplify. Enter the result as a single logarithm with a coefficient of 1. log; (2) – log; (5a®)

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