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zhannawk [14.2K]
3 years ago
10

If g(x) = 8x^6 and f(x) = log4 (2x) then f(g(x)) = ?

Mathematics
1 answer:
Lena [83]3 years ago
8 0

\begin{array}{llll} \textit{logarithm of factors} \\\\ \log_a(xy)\implies \log_a(x)+\log_a(y) \end{array} ~\hspace{4em} \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}

\begin{cases} g(x)=8x^6\\\\ f(x)=\log_4(2x) \end{cases}\qquad \qquad \begin{array}{llll} f(~~g(x)~~)=\log_4[~2g(x)~] \\\\\\ f(~~g(x)~~)=\log_4[~2(8x^6)~] \end{array} \\\\\\ f(~~g(x)~~)=\log_4(16x^6)\implies f(~~g(x)~~)=\log_4(4^2x^6) \\\\\\ f(~~g(x)~~)=\log_4(4^2)~~ + ~~\log_4(x^6)\implies \boxed{f(~~g(x)~~)=2~~ + ~~6\log_4(x)}

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What is the graph of the inequality 3x+2y>-5
Doss [256]

Answer:

The graph with solution is shown below.

Step-by-step explanation:

We need to find the x-intercept and y-intercept for given equation.

For  x-intercept , substitute y=0

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We get,

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3 years ago
Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that th
IgorLugansk [536]

Answer:

a) 0.32 = 32% probability that your bid will be accepted

b) 0.72 = 72% probability that your bid will be accepted

c) An amount in excess of $15,400.

Step-by-step explanation:

An uniform probability is a case of probability in which each outcome is equally as likely.

For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.

The probability that we find a value X lower than x is given by the following formula.

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You will win if the competitor bids less than 14000. So

P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72

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c. What amount should you bid to maximize the probability that you get the property (in dollars)?

His bid is uniformly distributed between $10,400 and $15,400.

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