# 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.

### 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:

### 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.

### 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.

### 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,

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