# Algebra II : Logarithms with Exponents

## Example Questions

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### Example Question #61 : Simplifying Logarithms

Use and Evaluate:       Explanation:

Since the question gives, and To evaluate manipulate the expression to use what is given.    ### Example Question #62 : Simplifying Logarithms

Simplify:       Explanation:

According to log rules, when an exponential is raised to the power of a logarithm, the exponential and log will cancel out, leaving only the power.

Simplify the given expression. Distribute the integer to both terms of the binomial.

The answer is: ### Example Question #63 : Simplifying Logarithms

Simplify:       Explanation:

The natural log has a default base of .

This means that the expression written can also be: Recall the log property that: This would eliminate both the natural log and the base, leaving only the exponent.

The natural log and the base will be eliminated.

The expression will simplify to: The answer is: ### Example Question #71 : Simplifying Logarithms

Simplify:       Explanation:

The log property need to solve this problem is: The base and the log of the base are similar.  They will both cancel and leave just the quantity of log based two. The answer is: ### Example Question #72 : Simplifying Logarithms

Solve:       Explanation:

Rewrite the log so that the terms are in a fraction. Both terms can now be rewritten in base two. The exponents can be moved to the front as coefficients. The answer is: ### Example Question #73 : Simplifying Logarithms

Which statement is true of for all positive values of ?      Explanation:

By the Logarithm of a Power Property, for all real , all   Setting , the above becomes Since, for any for which the expressions are defined, ,

setting , th equation becomes .

### Example Question #74 : Simplifying Logarithms

Which statement is true of for all integers ?      Explanation:

Due to the following relationship: ; therefore, the expression can be rewritten as By definition, .

Set and , and the equation above can be rewritten as ,

or, substituting back, 2 Next →

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