Thursday, June 26, 2008

1st question:
2log₃(x-1)-log₃(x+3)= 2

2nd question:
log₂(x+19)-log₂(3x-5) = 4 - log₂2(x-4)

Introduction
Logarithms are initially developed to reduce large numbers into smaller numbers, so that operations such as multiplication and division can be performed more efficiently. Do not forget that this is way before calculator is developed! When translated literally from the Chinese language, logarithm means reduced number.

The logarithmic form is another way of expressing the exponential form, this time in much smaller numbers. Like surds, most logarithms are irrational numbers.

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Laws of logarithms
log_amn = log_am + log_an
log_aa = 1
log_a(m/n) = log_am - log_an
log_a1=0
log_amⁿ = n log_am
Changing of Base
log_ab = log_cb / log_ca

Examples of solving logarithms:
log₂16 - log₂4
= log₂(16/4)
= log₂4
= 2

Solving unknowns in logarithms:
log₂(x+3) - log₂x = 2
log₂(x+3 / x) = 2
4 = (x+3) / x
4x = x+3
3x = 3
x = 1

Solving logarithms using change of base law:
log₄8 - log₂8
= log₂8 / log₂4 - log₂8
= 3/2 - 3
= -1.5


~~~ Welcome to the World Of Maths ~~~

Labels: Intro

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ZhengGuang(35), ShiJie(38), HongLiang(41)
Class 3F
Nan Chiau High School

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Huaan