Home >> PURE MATHS, Algebra, laws of exponentials & logarithms
first principles |
The Laws of Logarithms
Proofs
Changing the Base
Remember that the change of base occurs in the term where the base is 'x' or some other variable.
Example #1
Simultaneous Equations
'Substitution' simultaneous equations are common problems.
method:
| 1. first find what x is in terms of y |
| 2. then substitute for x in the other equation |
| 3. solve for y |
Example #1
Variable in the Index
method:
1. take logs on both sides |
2. move the indices infront of the logs |
3. expand the equation |
4. collect x-terms to the left |
| 5. sum the numbers to the right |
These problems can be tricky with the amount of arithmetic involved.
So make sure you write everything down to make checking your working easier.
Example #1
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