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Xelga [282]
3 years ago
7

2 log7 x=log7 27+log7 3

Mathematics
1 answer:
djverab [1.8K]3 years ago
7 0

Domain:x > 0\\\\2\log_7x=\log_727+\log_73\\\\\text{use}\ \log x^n=n\log x\ \text{and}\ \log x+\log y=\log(xy)\\\\\log_7x^2=\log_7(27\cdot3)\iff x^2=81\to x=\sqrt{81}\to\boxed{x=9}

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If we draw a rhombus OABC on a coordinate grid with one vertex at the point O (0,0)

and let its height be 1 then (using the Pythagoras theorem) the coordinates of the 4 points will be as follows:-

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Slope of the diagonal OB = 1 / (sqrt2 + 1)

Slope of the other diagonal AC = - 1 / (sqrt2 - 1)

Product of the slopes = - 1 / ( sqrt2 + 1)(sqrt2 - 1) = -1 / 1 = -1

This proves that the diagonals are perpendicular.

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2 years ago
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Step-by-step explanation:

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The third choice is correct

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