Algebra II : Log-Base-10
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Example Questions
Example Question #1 : Logarithms
Based on the definition of logarithms, what is 
10
2
4
100
3
3
For any equation 
Example Question #1 : Log Base 10
Evaluate 
Take the common logarithm of both sides, and take advantage of the property of the logarithm of a power:
Example Question #1 : Log Base 10
What is the value of 
Base-10 logarithms are very easy if the operands are a power of 
Becomes...
because
Applying logarithm rules, you can factor out the 
Now, 
Therefore, your answer is 
Example Question #1 : Log Base 10
What is the value of 
Round to the nearest hundreth.
Base-10 logarithms are very easy if the operands are a power of 
Becomes...
because
Applying logarithm rules, you can factor out the 
Now, 
Therefore, your answer is 
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:
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