# Logarithms and exponential functions

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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

Find the number of digits in the number 4^100

Find the first digit in the number 4^100

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#2

(Original post by

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

**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

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(Original post by

So how can you rexpress the things you're supposed to find in terms of log 4 (base 10) which you're given?

**mqb2766**)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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#4

(Original post by

Log 4 base 10 <2?

**Shas72**)Log 4 base 10 <2?

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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(Original post by

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

**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

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#6

(Original post by

I dont see any pattern. It's very random.

**Shas72**)I dont see any pattern. It's very random.

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#8

(Original post by

.

**hoosie**).

Last edited by mqb2766; 1 month ago

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#9

(Original post by

Can you pls delete and wait before expanding on the hint. The OP has not shown any working so far.

**mqb2766**)Can you pls delete and wait before expanding on the hint. The OP has not shown any working so far.

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#10

(Original post by

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.

**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.

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#11

(Original post by

The forum rules are clear. Please don't offer larger hints when help is already being supplied

**mqb2766**)The forum rules are clear. Please don't offer larger hints when help is already being supplied

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#12

(Original post by

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?

**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?

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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(Original post by

In future I will keep my hints

**hoosie**)In future I will keep my hints

(Original post by

**hoosie**)
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(Original post by

Can you pls delete and wait before expanding on the hint. The OP has not shown any

**mqb2766**)Can you pls delete and wait before expanding on the hint. The OP has not shown any

(Original post by

What did you get?

**mqb2766**)What did you get?

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(Original post by

Iam sorry for the late response. I had classes. I will look into the method you have mentioned and work out. Thanks a lottt

**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

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(Original post by

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.

**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.

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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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**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.

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#20

**Shas72**)

So according to the hint that you have provided it will be 100 log (base 10) 4=0.60206

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