What must logb 1 be equal to?

Q: Evaluate value of the following log9 x log3 x

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Q: Show that loga b logb a= I for all a, b > 0 such that a # 1 andb #1.

A: We will use the change of base formula

Q: use the properties of logarithms to expand log(z^5x)   log(z^5x)=

A: Answer: Solving the given integral by properties of logarithm as follows:

Q: Without using the theory of logarithms, show that for any natural number n, there exists a natural…

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

A: The given logarithmic equation is:  log z5xy3

Q: 101. Show that log,(x + V – 1) + log.(x - Vr - 1) = 0.

A: To show: loga(x+x2-1)+loga(x-x2-1)=0 Solution: loga(x+x2-1)+loga(x-x2-1)=0 Considering, Left Hand…

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

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Q: Use the properties of logarithms to expand the logarithmic expression.

A: Given : xlnx−4

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

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Q: Use the properties of logarithms to expand the logarithmic expression.

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Q: If f(x) = 1- log5 , then f-¹(x) =

A: Given that a function f(x)= 1 - log5x and we find f-1(x) .   Here i attached the solution of this…

Q: What is the base of the common log, log(x) What is the base of the natural log, In(x)?

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

A: Use property of log

Q: Suppose that, for a certain real number b > 0, log,(3) = 2.53 and log,(5) = 4.21 Find log,(45) 1…

A: Given:  logb3=2.53   and logb5=4.211) logb45=logb9×5we know that log(ab)=loga +logbThen…

Q: Show that, log(-1+i)² + 2log(–1+i).

A: Use the formula logz=lnr+iθ. To find log-1+i2:…

Q: Let u = In a and v In b. Write the expression in terms of u and v without using the logarithm…

A: We use the multiplication principle of logarithm

Q: a. Use a chain of equal expressions to show that for all x-values such that x> 0, = x+In(x) – 6ln(x+…

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Q: Use the properties of logarithms to expand log (zy).

A: Properties of Logarithms :i) log(ab) = log(a) + log(b)ii) log(ab) = b log(a)

Q: Show that loga b logb a= I for all a, b > 0 such that a ≠ 1 and b ≠. 1

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Q: Use the Laws of Logarithms to combine the expression. 4 log(x) -- log(x2 + 1) + 4 log(x – 1)

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Q: Use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.…

A: Log(m)+ log(n)=log(mn) Log(m)-log(n)=log(m/n)

Q: Use the Laws of Logarithms to expand the expression. log z2

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Q: snip

A: Prove that: logaMN=logaM-logaN, where a, M and N are positive real numbers and a≠1

Q: Use log, 20.401, log, 3≈ 0.503, and log, 5 0.794 to approximate the value of the given logarithm to…

A: Given : logb2≈.401 , logb3≈.503 and logb5≈.794 To find : logb75≈?

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

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Q: Use the Laws of Logarithms to expand the quantity.          ____In  √ab

A: We have to expand ln ab

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

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Q: use the definition of the logarithmic function to find X A) in x =3 B) in e^2 = x

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

A: log (a.b) = log (a) + log (b) log (an)= n.log(a)

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

A: properties of logarithms are logcab=logca-logcb logcab=logca+logcb logaxb=b·logax

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

A: logan=nloga   logab=loga-logb

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: log 3)

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Q: Let a ER. Solve the inequality for real values of x. log[x] (x − a) +log[x] (x+a) <0 [...] floor…

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

A: To Show: loga1N=-logaN, where a and N are positive real number and a≠1. Concept: i.…

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

A: Given,           logx4y5

Q: Prove that log(7) is irrational. Hint: Use contradiction and the definition of a logarithm to prove.

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

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Q: Show that, log(-1+i)² # 2log(-1+i).

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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

A: Now,  we will expand the logarithm using logarithm formula.

Q: Use log,4 s 0.712 and log,5 s 0.827 to evaluate log, 25. 1.54 0.827 0.589 1.654

A: Find the value of log 25 base 7

Q: a) log2 25 – log, 5 is the base 2 logarithm of ) 4 In x + In(x – 25) is the base e logarithm of

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Q: Use the properties of logarithms to rewrite the expression as the logarithm of a single quantity.…

A: we have to write in single term of given expression

Q: Use the Laws of Logarithms to expand the expression. In √ab

A: Given: The expression lnab. The given expression can be expanded as, lnab=lnab12…

Q: Use log, 3 z 0.5869 and log, 5 z 0.8598 to find an approximate value for V5 logb 9

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Q: Find the largest value of xx that satisfies: log5(x^2)−log5(x+3)=9 x=

A: For the solution follow the next step.

Q: Use the definition of the logarithmic function to find x. In x = -1 In (1/e) = x %3D

A: First Part: Given, lnx=-1x=e-1lnex=a⇒x=eax=1e

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

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