12.) Use the laws of logarithms to combine: 2 log x + 1 log(x² + 1)

Q: 13. Combine the following into a logarithm: single 2 log – 3 log y + log(x*y²)

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Q: 11. Express as a single logarithm and simplify if possible. log (x2 – 5x – 14) – log (x² – 4)

A: Given query is to simplify the logarithmic expression.

Q: 2 Find x so that log10 x = log, 10

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Q: 3 – log,(2x) = log:(x – 4)

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

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Q: 15) Use the properties of logarithms to rewrite each 2 a. In c. In 5y b. In Vr+2 d. In ¤(x +1)´

A: Explanation and solutions is given below....

Q: Show that, log5 x can be expressed as 2 log, x, where b> 0.

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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: 4. If log,v=log,x - (2logby +logbz) , what is the value of v?

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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: 8. If logax = loga6, then x = M 9. logaN In 8 10. True or False. = 2. In 4

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Q: 6. A. Apply the properties of logarithms to expand the following expressions and simplify as much as…

A: Apply logab= loga + logb           loga/b=loga-logb

Q: how do i condense this expression to a single logarithm? step by step please

A: The given logarithmic expression is

Q: B. Find the sum of the solutions to the logarithmic equation 2log 102-3 log r+2(log :)2 where log r…

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Q: 1. Show that (a) Log(-ei) = 1 - ži;

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Q: 8. Use the properties of logarithms to expand the following into a sum or difference of logarithms.…

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

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Q: (a) In (x (b) log; 2y2

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Q: Suppose that a and y are real numbers such that log2 (x) = – 3 and log2 (y) 6. Calculate the…

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Q: 4. Determine the co-ordinates of the point of intersection of the graphs of f(x) = 5(3*) %3D log a…

A: The given curves are  f(x) = 5.3x f(x) = 7.2x

Q: Prove that | log,x| E O(log2 x )

A: It is obvious that log2x≤log2x so, log2x∈Olog2x.

Q: 2 log, (x) = 2

A: The given equation is: 2 log4(x) = 2

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

A: Introduction :

Q: 4. What is b if (log, x)' :? Зх

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

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

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Q: #12. SOLVE THE EQUATION а. log (x²) = (log x)² 1 or 100 b. log Vr – 9 = 2 V 10,009 С. log (x³) =…

A: Since you have posted multiple subparts, as per our policy we will answer first three subparts.…

Q: 11. Write as a single logarithm: 1 log2 X +3 log2 Y - 3 ·log2 Z

A: To write: The expression 13log2X+3log2Y-52log2Z in single logarithm. Formula used: Logarithmic rule:…

Q: The solution of the logarithmic equation log z + log(x + 5) = log 24 is 3. 11 O16

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Q: 17. Find the value of x without the use of calculator 1 log, 3. 4

A: Given:

Q: (2) Combine the following into one single logarithm with a coefficient of 1 in front of the entire…

A: 6log4x-5-34logx+log9x-1

Q: 26. Describe the behavior of each of the following: (a) 5 (b) log x as x>0 as x (c) ln x as x ->co…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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

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Q: a- Simply the following 1. Inx – In(x2 – 1) + 2ln(x + 3) 2. 5log2 + log3 - log8

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

A: The given function,   f(x)=logx-4

Q: Express log(x²-x-12) - log(x² - 7x + 12) as a single logarithm. State any restrictions on the…

A: Given : expression  logx2-x-12-logx2-7x-12 Prerequisite : Here we use the formula log a - log b =log…

Q: . Use the Laws of Logarithms to expand the expression.

A: We have to use the laws of logarithms to expand the expressions: a logxy3z2      b lnxy     c…

Q: 9. Express equivalent expression: log(x – 3) – log() + log 4 as an x+3

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Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

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Q: Expand the logarithm fully using the properties of logs. Express the final answer in terms of log x,…

A: Explanation of the answer is as follows

Q: 4. Condense the log to a single log expression. a. 2 log y - 3 log x - 2 log 10 b. Ina+3 ln y

A: See this solution in below

Q: 1. solve for x, log2(3x-2)=4.    2. use the laws of logarithims to rewrite 7log x - 3log y as a…

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

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Q: Prove that| log,x E O(log2 x)

A: We know the relation |_log2x_|≤log2x≤ log2x. That is the floor value of any real number is less than…

Q: b) Find the value of x that satisfies log(x+3)− log x = log x+log 2.

A: Follow the procedure given below.

Q: 12.) Use the laws of logarithms to combine: 1 2 log x log(x² + 1) - 2

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

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Q: 2. Use the properties of logarithms to condense the expressions as a single logarithm. 4. log a – 3…

A: We have to solve given logarithmic expression.

Q: Express in logarithmic form. 8 64 4. Express the following in expanded form. UV logB W. 3.

A: Dear student, You have posted many questions, in our policy we are providing to you first two…

Q: (a) Prove that log₁ x= -log₁ x where a > 1. a

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