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secondary 3 | A Maths
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need help with these qns, pls explain too
for 15b i only managed to get 1 answer when there is 2 (ans : 4 or 2, only got 2)
Date Posted: 3 years ago
Views: 512
15b)
log2(x) + 2 / log2(x) = 3
Typically we'll use the substitution u = log2(x)
u + 2/u = 3
Multiply both sides by u,
u² + 2 = 3u
u² - 3u + 2 = 0
(u - 2)(u - 1) = 0
u = 2 or u = 1
Sub back u = log2(x),
log2(x) = 2 or log2(x) = 1
x = 2² or x = 2¹
x = 4 or x = 2
log2(x) + 2 / log2(x) = 3
Typically we'll use the substitution u = log2(x)
u + 2/u = 3
Multiply both sides by u,
u² + 2 = 3u
u² - 3u + 2 = 0
(u - 2)(u - 1) = 0
u = 2 or u = 1
Sub back u = log2(x),
log2(x) = 2 or log2(x) = 1
x = 2² or x = 2¹
x = 4 or x = 2
See 3 Answers
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For Qn12, you will need to refer to the laws of indices.
For Qn13, you will also need to refer to the laws of indices.
Take note that if the "big number" (in this case, 5) is the same throughout the equation e.g. 5^2a ÷ 5^3b = 5^0 (second line of Answer 13), there is a law that you can use which states that the addition/subtraction of the powers on the left side equals to the addition/subtraction of the powers on the right side. (in this case, it is subtraction for the left side because ÷ means -).
* multiplying the same "big numbers" with powers e.g. 5^2 x 5^3 -> adding of powers (5^5)
* dividing the same "big numbers" with powers e.g. 5^2 / 5^3 -> minusing of powers (5^-1)
For Qn13, you will also need to refer to the laws of indices.
Take note that if the "big number" (in this case, 5) is the same throughout the equation e.g. 5^2a ÷ 5^3b = 5^0 (second line of Answer 13), there is a law that you can use which states that the addition/subtraction of the powers on the left side equals to the addition/subtraction of the powers on the right side. (in this case, it is subtraction for the left side because ÷ means -).
* multiplying the same "big numbers" with powers e.g. 5^2 x 5^3 -> adding of powers (5^5)
* dividing the same "big numbers" with powers e.g. 5^2 / 5^3 -> minusing of powers (5^-1)
Date Posted:
3 years ago
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Refer to logarithm & indices laws.
Make sure that the base numbers are same (in this case "2") so that you can apply the laws easily.
Make sure that the base numbers are same (in this case "2") so that you can apply the laws easily.
Date Posted:
3 years ago
e^2e^x=e^4y is the same as e^2 x e^x = e^4y?
yes, they are the same. Just that they didn't add the "x" sign.
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Refer to logarithm laws.
Do let me know if there are any parts that confuse you, i'll try my best to explain those areas.
Do let me know if there are any parts that confuse you, i'll try my best to explain those areas.
Date Posted:
3 years ago
at the 3rd to 4th part why the 1/2 become 2 tho
1 divided by 1/2 gives you 2
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