# Logarithms and exponential functions

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#1
Given that log4 base 10 =0.60206, correct to 5 dp and that 10^0.206<2 ,without using calculator
Find the number of digits in the number 4^100
Find the first digit in the number 4^100
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1 month ago
#2
(Original post by Shas72)
Given that log4 base 10 =0.60206, correct to 5 dp and that 10^0.206<2 ,without using calculator
Find the number of digits in the number 4^100
Find the first digit in the number 4^100
So how can you rexpress the things you're supposed to find in terms of log 4 (base 10) which you're given?
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#3
(Original post by mqb2766)
So how can you rexpress the things you're supposed to find in terms of log 4 (base 10) which you're given?
Log 4 base 10 <2?
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1 month ago
#4
(Original post by Shas72)
Log 4 base 10 <2?
Certainly correct, but not necessarliy useful.

You want to work out the number of digits in 4^100.
How is that related to log 4 (base 10)?

If you're unsure, try thinking about the definition of logs (and their inverse), or even simplifying the problem to considering 4^1, 4^2, 4^3, 4^4 ... instead of 4^100 and see if you can spot a pattern
Last edited by mqb2766; 1 month ago
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#5
(Original post by mqb2766)
Certainly correct, but not necessarliy useful.

You want to work out the number of digits in 4^100.
How is that related to log 4 (base 10)?

If you're unsure, try thinking about the definition of logs (and their inverse), or even simplifying the problem to considering 4^1, 4^2, 4^3, 4^4 ... instead of 4^100 and see if you can spot a pattern
I dont see any pattern. It's very random.
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1 month ago
#6
(Original post by Shas72)
I dont see any pattern. It's very random.
What did you get?
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1 month ago
#7
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1 month ago
#8
(Original post by hoosie)
.
Can you pls delete and wait before expanding on the hint. The OP has not shown any working so far.
Last edited by mqb2766; 1 month ago
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1 month ago
#9
(Original post by mqb2766)
Can you pls delete and wait before expanding on the hint. The OP has not shown any working so far.
OP has not shown any working so far because they’re not sure how to proceed. I decided to go a little further (with a little example) to help explain what you meant by your hint. I just thought the student wasn’t sure what to do. I don’t think what I did hampered the OP’s learning in any way. In fact their understanding of how to proceed would have become clearer to them after reading my post. I have taken onboard what you said to me in the past and so made sure my response was for the benefit of the student. We’re all here to help aren’t we? That’s what I was trying to do.
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1 month ago
#10
(Original post by hoosie)
OP has not shown any working so far because they’re not sure how to proceed. I decided to go a little further (with a little example) to help explain what you meant by your hint. I just thought the student wasn’t sure what to do. I don’t think what I did hampered the OP’s learning in any way. In fact their understanding of how to proceed would have become clearer to them after reading my post. I have taken onboard what you said to me in the past and so made sure my response was for the benefit of the student. We’re all here to help aren’t we? That’s what I was trying to do.
The forum rules are clear. Please don't offer larger hints when help is already being supplied.
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1 month ago
#11
(Original post by mqb2766)
The forum rules are clear. Please don't offer larger hints when help is already being supplied
But what if I believe your hint didn’t help the student to proceed? That’s the reason I chose to provide a simple example for the student to follow so that they could make use of your hint. Surely explaining a hint better to the OP so that they actually receive help is not against forum rules?
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1 month ago
#12
(Original post by hoosie)
But what if I believe your hint didn’t help the student to proceed? That’s the reason I chose to provide a simple example for the student to follow so that they could make use of your hint. Surely explaining a hint better to the OP so that they actually receive help is not against forum rules?
The OP can say this without assuming it.

Sometimes the hardest part is getting started and the OP may not really understand your example and simply sub the numbers in, which seems to be what you're encouraging.

The forum rules state that a minimum hint should be offered. This isn't what you're doing.
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1 month ago
#13
In future I will keep my hints to a minimum.
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#14
(Original post by hoosie)
In future I will keep my hints
(Original post by hoosie)
Iam sorry for the late response. I had classes. I will look into the method you have mentioned and work out. Thanks a lottt
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#15
(Original post by mqb2766)
Can you pls delete and wait before expanding on the hint. The OP has not shown any
(Original post by mqb2766)
What did you get?
Iam sorry for the delayed response. I had to attend classes. So when I saw the pattern of 4^1 to 4^10 it was like 1, 2,2,3,4,4,5,5,6,7 respectively
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#16
(Original post by Shas72)
Iam sorry for the late response. I had classes. I will look into the method you have mentioned and work out. Thanks a lottt
So according to the hint that you have provided it will be 100 log (base 10) 4=0.60206
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#17
(Original post by hoosie)
As shown by OP’s last response my hint has given them the encouragement to proceed which is what I wanted, If they are not sure how to apply my example and have shown where they’re stuck I can provide more explanation.
It would be very very helpful if you can pls provide more explanation as iam not able to understand the question. Thanks a tonne
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#18
This is specifically difficult as we cant use the calculator. So I want to know the method so that I can apply to other problems too
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#19
(Original post by hoosie)
As shown by OP’s last response my hint has given them the encouragement to proceed which is what I wanted, If they are not sure how to apply my example and have shown where they’re stuck I can provide more explanation.
So log (base 10) 4 =0.60206 so 4= 10^0.60206
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1 month ago
#20
(Original post by Shas72)
So according to the hint that you have provided it will be 100 log (base 10) 4=0.60206
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