What is the length of the missing side, x? I would really appreciate the help.

Mathematics

1 answer:

BlackZzzverrR [31]2 years ago

5 0

Answer:

x/40=49/35

49×40=x×35

x=(49×40)÷35

x=56

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Pair-1: $log_{2}x = 5$ ↔ 32
Pair-2: $log_{10}x = 3$ ↔ 1000
Pair-3: $log_{4}x = 2$ ↔ 16
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Explanation:

Pair-1:
$log_{2}x = 5 \\ \frac{ln(x)}{ln(2)} = 5 \\ ln(x) = 5 * ln(2) \\ x = e^{5*ln(2)} \\ x = 32$

Pair-2:
$log_{10}x = 3 \\ \frac{ln(x)}{ln(10)} = 3 \\ ln(x) = 3 * ln(10) \\ x = e^{3*ln(10)} \\ x = 1000$

Pair-3:
$log_{4}x = 2 \\ \frac{ln(x)}{ln(4)} = 2 \\ ln(x) = 2 * ln(4) \\ x = e^{2*ln(4)} \\ x = 16$

Pair-4:
$log_{5}x = 4 \\ \frac{ln(x)}{ln(5)} = 4 \\ ln(x) = 4 * ln(5) \\ x = e^{4*ln(5)} \\ x = 625$

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You plug -x+16 in for y in x+4y=37 to get x after you multiply x+4y=37 by -1.
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