# Maths HELP

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A sum of money is invested in a savings account withba compound interest rate of r% paid annually. T is the number of years taken for the investment to be worth twice the sum invested.a) Express in the form loga(b) where b is an integer.b) Money invested in a simple interest account with an annual interest rate of p% takes twice as long to double in value as money in a compound interest account with annual interest rate q%End of QSo far for part a ive gotten T=log2/log(100 r/100) but idk how to simplify furtherBut for part b i have no idea where to start

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(Original post by

A sum of money is invested in a savings account withba compound interest rate of r% paid annually. T is the number of years taken for the investment to be worth twice the sum invested.a) Express in the form loga(b) where b is an integer.b) Money invested in a simple interest account with an annual interest rate of p% takes twice as long to double in value as money in a compound interest account with annual interest rate q%End of QSo far for part a ive gotten T=log2/log(100 r/100) but idk how to simplify furtherBut for part b i have no idea where to start

**hiya**)A sum of money is invested in a savings account withba compound interest rate of r% paid annually. T is the number of years taken for the investment to be worth twice the sum invested.a) Express in the form loga(b) where b is an integer.b) Money invested in a simple interest account with an annual interest rate of p% takes twice as long to double in value as money in a compound interest account with annual interest rate q%End of QSo far for part a ive gotten T=log2/log(100 r/100) but idk how to simplify furtherBut for part b i have no idea where to start

Last edited by mqb2766; 2 weeks ago

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**mqb2766**)

Can you change the base in a). If b is an integer it suggests base a is a function of r? Are you sure a) is T = , can you upload a pic of the question?

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y = a^x

Then

log_a(y) = x

That's all they've done? x is T, y is 2 and the base a is (100+r)/100. If you'd taken logs with a different base, use the base change formula.

It is an unusual question, in that the base is a function of a variable.

Last edited by mqb2766; 2 weeks ago

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(Original post by

So what is confusing? If you have

y = a^x

Then

log_a(y) = x

That's all they've done? x is T, y is 2 and the base a is (100+r)/100. If you'd taken logs with a different base, use the base change formula.

It is an unusual question, in that the base is a function of a variable.

**mqb2766**)So what is confusing? If you have

y = a^x

Then

log_a(y) = x

That's all they've done? x is T, y is 2 and the base a is (100+r)/100. If you'd taken logs with a different base, use the base change formula.

It is an unusual question, in that the base is a function of a variable.

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#7

(Original post by

I understand the process of getting T=log base(100+r)/100 (2) in the required form but I was confused at how the mark scheme simplified T=log2/log(100+r)/100 into the required form..

**hiya**)I understand the process of getting T=log base(100+r)/100 (2) in the required form but I was confused at how the mark scheme simplified T=log2/log(100+r)/100 into the required form..

http://home.windstream.net/okrebs/page57.html

Last edited by mqb2766; 2 weeks ago

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(Original post by

As in the previous reply, either use the log definition directly or use the change of base formula:

http://home.windstream.net/okrebs/page57.html

**mqb2766**)As in the previous reply, either use the log definition directly or use the change of base formula:

http://home.windstream.net/okrebs/page57.html

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