Log Function (1 Viewer)

[danster]

I know it is not part of the syllabus to learn how to use the Log function, but it sure beats trial and error and saves plenty of time. Could anyone clarify how to use the function again?!

Thanks.

 

[PC]

Probably the only time you will need to use logs is with exponential equations and applications such as declining balance depreciation.

Basically, if a = b^x then x = log a/log b.

1. If 10^x = 100, find x.

Since 10^x = 100, then x = log 100/log 10 = 2 (which we knew anyway).

2. How long does it take an investment of $1000 to double in value if it is invested at 12% p.a., compounded monthly?

Interest rate = 12% p.a. = 1% per month = 0.01 as a decimal
Since we need $1000 to double, we know that A = $2000.

A = P(1 + r)ⁿ
2000 = 1000(1 + 0.01)ⁿ
2000 = 1000(1.01)ⁿ
Divide by 1000 gives:
2 = 1.01ⁿ
or:
1.01ⁿ = 2

So:
n = log 2/log 1.01
n = 69.66071689 months
n = 5 years 10 months (roughly)

 

[Tommy_69]

thanks mate that will be v useful because i use trial and error a lot and it takes up time!

 

[redruM]

2 = 1.01ⁿ

at this stage consider, taking the log of both sides.

.'. log 2 = log (1.01)ⁿ

here we use the rule, log aⁿ = n x log a.

.'. log 2 = n x log (1.01)

then it comes back to the same way as shown by pc,

n = log 2/ log 1.01

edit 1: when doing this keep in mind you cannot take the log of a negative number, ie log ( < 0). if you do get this, you have made a mistake in leading up to when you take the log.

edit 2: use the two methods together, to make sure you are doing it right.