Algebra II : Natural Log

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #21 : Natural Log

Solve:  

Possible Answers:

Correct answer:

Explanation:

In order to eliminate the natural log, which has a base of , we will need to raise both side as powers of .

The equation can be simplified to:

Add  on both sides.

Divide by two on both sides.

The answer is:  

Example Question #22 : Natural Log

Try without a calculator:

Which expression is not equivalent to 1?

Possible Answers:

Correct answer:

Explanation:

 is the correct choice.

For all  for which the expressions are defined, 

.

Setting , this equation becomes

 - that is, the one thousandth root of 1,000. This is not equal to 1, since if it were, it would hold that  - which is not true. 

 

Of the other four expressions:

, the common, or base ten, logarithm of 10, can be rewritten as , and , the natural, or base , logarithm of , can be rewritten as . A property of logarithms states that for all . Therefore,  and  .

 

, since any nonzero number raised to the power of 0 is equal to 1.

 

By the Power of a Power Property, 

, so

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