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secondary 3 | A Maths
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need help w this qn,, pls explain too
i dont even know how to start the qn
Date Posted: 3 years ago
Views: 296
I will look at this later.
Part 3c, the graph of y = - ./x is also not in your syllabus.
Part 3c, the graph of y = - ./x is also not in your syllabus.
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Parts a and b
Date Posted:
3 years ago
i dont rly understand 5a(i) the log48 part
Suppose that log 4 8 has a value x.
When you convert this to index form, it becomes 4^x = 8. In other words, we need to find the power of x such that 4^x = 8.
What would you do in this situation?
Well, you would convert everything to base 2.
(2^2)^x = 2^3
2^2x = 2^3
Comparing powers,
2x = 3
x = 3/2
So log4 8 = 3/2.
Now, the above that I have typed out is actually one way of evaluating log4 8. Another way, by logarithms which I have written, is related to this approach which I have typed out above.
Think of why I choose base 2.
By analogy, we use base 2 for log4 8.
Have you learnt the change of base rule (loga b = logc b / logc a)?
If yes, that's what I did here, where I converted the log to a common base 2 in both the numerator and the denominator.
When you convert this to index form, it becomes 4^x = 8. In other words, we need to find the power of x such that 4^x = 8.
What would you do in this situation?
Well, you would convert everything to base 2.
(2^2)^x = 2^3
2^2x = 2^3
Comparing powers,
2x = 3
x = 3/2
So log4 8 = 3/2.
Now, the above that I have typed out is actually one way of evaluating log4 8. Another way, by logarithms which I have written, is related to this approach which I have typed out above.
Think of why I choose base 2.
By analogy, we use base 2 for log4 8.
Have you learnt the change of base rule (loga b = logc b / logc a)?
If yes, that's what I did here, where I converted the log to a common base 2 in both the numerator and the denominator.
So, changing to base 2.
log4 8
= log2 8 / log2 4 (my a is 4, my b is 8, my c is 2)
Then, I rewrote 8 as 2^3 and 4 as 2^2 before proceeding with the bring-down power rule.
log4 8
= log2 8 / log2 4 (my a is 4, my b is 8, my c is 2)
Then, I rewrote 8 as 2^3 and 4 as 2^2 before proceeding with the bring-down power rule.
thx :)
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I will still draw the graph of y = - ./x for your reference even though it’s no longer in your syllabus.
Date Posted:
3 years ago
for 3lnx does the graph look the same as y=logax for a>1 even if theres a number infront (3)
The multiplier "3" in front actually "stretches" a graph in the vertical direction, so it looks more elongated. Imagine Tom and Jerry where Tom gets "elongated" in height.
For your sketching for the single ln graph, we can't distinguish it from other ln graphs. As such, we just sketch the graph as though the equation is y = ln x.
For your sketching for the single ln graph, we can't distinguish it from other ln graphs. As such, we just sketch the graph as though the equation is y = ln x.
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In case you were wondering, this is how the multiplier in front (the coefficient of loga x) affects the graph.
Date Posted:
3 years ago
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Effect of changing the base
Date Posted:
3 years ago
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Effect of changing the contents in the ln
Date Posted:
3 years ago
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