Algebra II : Simplifying Logarithms

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #131 : Logarithms

Simplify:  

Possible Answers:

Correct answer:

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 #14 : Logarithms With Exponents

Solve:  

Possible Answers:

Correct answer:

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 ?

Possible Answers:

Correct answer:

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 #15 : Logarithms With Exponents

Which statement is true of 

for all integers ?

Possible Answers:

Correct answer:

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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