Algebra II : Log-Base-10

Study concepts, example questions & explanations for Algebra II

varsity tutors app store varsity tutors android store

Example Questions

Example Question #11 : Log Base 10

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

In order to eliminate the log based ten, we will need to raise both sides as the exponents using the base of ten.

The equation becomes:

The ten and log based ten will cancel, leaving just the power on the left side.  Change the negative exponent into a fraction on the right side.

Divide by two on both sides, which is similar to multiplying by a half on both sides.

Simplify both sides.

The answer is:  

Example Question #12 : Log Base 10

What is the value of  ?

Possible Answers:

Correct answer:

Explanation:

In order to solve this, we will need to rewrite the base  as , since log is by default base 10.

Rewrite the expression.

By log rules, the exponent can be pulled down as the coefficient.

The answer is:  

Example Question #11 : Log Base 10

Simplify 

Possible Answers:

Correct answer:

Explanation:

One of the properties of logs is the ability to cancel out terms based on the base of the log. Since the base of the log is 10 we can simplify the 100 to 10 squared.

 

The log base 10 and the 10 cancel out, leaving you with the value of the exponent, 2 as the answer.

Example Question #14 : Log Base 10

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

The log term has a default base of 10.  The 1000 will need to be rewritten as base 10.

Raise the coefficient of the log term as the power.

According to the log property:

The log based 10 and the 10 inside the quantity of the log will cancel, leaving just the power.

The answer is:  

 

Example Question #15 : Log Base 10

Simplify:  

Possible Answers:

Correct answer:

Explanation:

The log has a default of base ten.  This means we should convert the 1000 to a common base 10.

Replace this value inside the log term.

Since the log base 10 and the ten to a certain power are existent, they will both cancel, leaving just the power itself.

The answer is:  

Example Question #16 : Log Base 10

Solve:  

Possible Answers:

Correct answer:

Explanation:

Change the base of the inner term or log to base ten.

According to the log property:

The log based ten and the ten to the power of will cancel, leaving just the power.

The answer is:  

Example Question #17 : Log Base 10

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

Rewrite the log such that it is in its simplest form.  Break up the 500 with common factors.

This can be broken into addition of logs.

The answer is:  

Example Question #18 : Log Base 10

Solve the equation:  

Possible Answers:

Correct answer:

Explanation:

When the inner terms of a log are divided, we can simply rewrite separate logs using subtraction.

Note that log has a default base of ten, and we can rewrite the 1000 as ten to the power of three.

Use the property  to simplify the second term.

The answer is:  

Example Question #19 : Log Base 10

Simplify:   

Possible Answers:

Correct answer:

Explanation:

The log is in default base 10.  To simplify this log, we will need to change the base of 100 to base 10.

Rewrite the inner quantity.

We can use the additive rule of exponents since both bases are the same.

According to the rule of logs, a log of a base with similar bases will cancel, and will leave only the power.

The answer is:  

Example Question #20 : Log Base 10

Evaluate:  

Possible Answers:

Correct answer:

Explanation:

In order to eliminate the log, which has a default base of 10, we will need to raise both sides of the equation as powers using the value of 10.

The equation becomes:

Divide by three on both sides.

The answer is:  

Learning Tools by Varsity Tutors