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Exponentials & Logs : Logarithms
 

[ laws ][ proofs ][ base change ][ simult.eqs ][ x in index ]

 

 

 

 

The Laws of Logarithms

laws of logarithms

Proofs

number division and log subtratraction

 

change of base proof

 

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Changing the base

Remember that the change of base occurs in the term where the base is 'x' or some other variable.

Example #1

logarithm problem#1

 

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Simultaneous equations

'Substitution' simultaneous equations are common problems. First find what x is in terms of y. Then substitute for x in the other equation. Solve for y.

Example #1

logarithm problem#2

 

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Variable in the index

Take logs on both sides. Move the indices infront of the logs. Expand the equation. Collect x-terms to the left. 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

logarithm problem#3

 

 

 

 

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