PreCalculus Lesson 21 & 22 – Helpful Hints

Logarithmic Rules (Laws):

Power Rule:

Product Rule:

Quotient Rule:

Use Log rules to rewrite expressions.

To expand, first rewrite any radical using fractional exponents, then use the quotient rule, then the product rule, then the power rule.

Solve for x using the laws.
First write as a single log by using the power rule, then product rule, then the quotient rule. Once it is a single log, write it as an exponential problem.

It is important to note that you cannot take the log of a negative number. For example log(-4) is not possible.

You would solve natural log equations in the same manner. The natural log has an understood base of e.

Solving exponential equations:
Take the log (or ln) of both sides. Use the power rule. If there is more than one variable, then move the variable to one side and factor out the variable.

If the problem can be rewritten so that they have the same base:

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