prove why it is always true that b ^ logb⁡ (x) = x.

Q: If f(x) = log(a)x, show that f(x^α) = αf(x).

A: Given that:

Q: if y=logax, then y=a^x

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Q: PROVE that log5 100 = 2(1 + log5 2)

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Q: if log x^13 y^10/z^13 =A log(x)+B log(y)+C log(z) then A= B= C=

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Q: Determine if the following statements are True or False. Assume all values of the variables and…

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Q: Let b be a real number. By considering properties of exponential functions, show that the points…

A: We know, for any real number b > 1,         b0 = 1      => logb(b0) = logb(1)       =>…

Q: find range of the following function log_(4)|x+(1)/(x)|

A: We have to find range of the given function.

Q: Let y = f(x) be the function. Use the definition of the logarithm to obtain the inverse functions x…

A: Solving

Q: y=log_((1)/(4))(x). Write your answer only as an interval in the corroctlv written answer: (-inf,…

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Q: Prove that log b (a ^c)=c log b(a)

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Q: Which of the following functions are qx²)? ☐ 1x) = 17x + 11 (x) = x² +1000 f(x) = x logx (x) = x^/2…

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Q: For the function f(x)=log_((1)/(3))(x)+3, determine whether the function is increasing or…

A: The given function fx=log13x+3. We have determine whether the function is increasing or decreasing.

Q: for a function f(x) = log 1/4 (x) and g(x) =log^4(x), where is f>g and g>f

A: This is the problem of real-valued function.

Q: Solve ln (x-1) = 2 In (x+1) 2 ln (logx) = -> include restrictions for both

A: A and B calculations

Q: *If log(67) + log(y) = log(z), then 67 + y = z. a) True  b)False*If ln(67x) = ln (y), then 67x = y.…

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