Algebra II : Algebra II
Study concepts, example questions & explanations for Algebra II
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Example Questions
Example Question #1 : Log Base 10
Many textbooks use the following convention for logarithms:
What is the value of 
Remember:
So when we ask "What is the value of 
From this, it should be easy to see that 
Example Question #1 : Log Base 10
Evaluate the following expression:
Without a subscript a logarithmic expression is base 10.
The expression 
The logarithmic expression is asking 10 raised to what power equals 1000 or what is x when
We know that
so
Example Question #7 : Log Base 10
Assuming the value of 
Rewrite the logarithm in division.
As a log property, we can pull down the exponent of the power in front as the coefficient.
Cancel out the 
The answer is:
Example Question #8 : Log Base 10
Solve the following:
When the base isn't explicitly defined, the log is base 10. For our problem, the first term
is asking:
For the second term,
is asking:
So, our final answer is
Example Question #2 : Log Base 10
Which of the following expressions is equivalent to the expression 
None of the other choices is correct.
By the reverse-FOIL method, we factor the polynomial as follows:
Therefore, we can use the property
as follows:
Example Question #4 : Log Base 10
Evaluate 
The first thing we can do is bring the exponent out of the log, to the front:
Next, we evaluate 
Recall that log without a specified base is base 10 thus
Therefore
becomes,
Finally, we do the simple multiplication:
Example Question #11 : Log Base 10
Evaluate:
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 
In order to solve this, we will need to rewrite the base 
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
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:
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:
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