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Ainat [17]
3 years ago
10

Express 0.77230.77230, point, 7723 as a fraction

Mathematics
1 answer:
cricket20 [7]3 years ago
8 0

Answer:

7723/10000

Step-by-step explanation:

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Find the logarithmic function y = logbx that passes through the points
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b\in(0,\ 1)\ \cup\ (1,\ \infty)\\x > 0\\y\in\mathbb{R}\\--------------------------\\\\y=\log_bx\\\\For\ (1,\ 0)\to x=1,\ y=0.\ Substitute:\\\\\log_b1=0\to b^0=1\to b\in(0,\ 1)\ \cup\ (1,\ \infty)\\\\For\ (116,\ 2)\to x=116,\ y=2.\ Substitute:\\\\\log_b116=2\to b^2=116\to b=\sqrt{116}\\\to b=\sqrt{4\cdot29}\to b=\sqrt4\cdot\sqrt{29}\to b=2\sqrt{29}\\\\For\ (4,\ -1)\to x=4,\ y=-1.\ Substitute:\\\\\log_b4=-1\to b^{-1}=4\to b=\dfrac{1}{4}

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<h3>Then we have the answer:</h3>

\boxed{y=\log_{\frac{1}{4}}x}

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