All High School Math Resources
Example Questions
Example Question #1 : Multiplying And Dividing Logarithms
Simplify .
Using properties of logs we get:
Example Question #1 : Simplifying Logarithms
Simplify the following expression:
Recall the log rule:
In this particular case, and . Thus, our answer is .
Example Question #2 : Simplifying Logarithms
Use the properties of logarithms to solve the following equation:
No real solutions
Since the bases of the logs are the same and the logarithms are added, the arguments can be multiplied together. We then simplify the right side of the equation:
The logarithm can be converted to exponential form:
Factor the equation:
Although there are two solutions to the equation, logarithms cannot be negative. Therefore, the only real solution is .
Example Question #2 : Simplifying Logarithms
Which of the following represents a simplified form of ?
The rule for the addition of logarithms is as follows:
.
As an application of this,.
Example Question #1 : Adding And Subtracting Logarithms
Simplify the expression using logarithmic identities.
The expression cannot be simplified
The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator.
If we encounter two logarithms with the same base, we can likely combine them. In this case, we can use the reverse of the above identity.
Example Question #1 : Simplifying Logarithms
Evaluate by hand
Cannot be found by hand
Using the logarithm rules, exponents within logarithms can be removed and simply multiplied by the remaining logarithm. This expression can be simplified as
Example Question #151 : Algebra Ii
Solve for
Use the power reducing theorem:
and
Example Question #1 : Simplifying Logarithms
Which of the following expressions is equivalent to ?
According to the rule for exponents of logarithms,. As a direct application of this,.
Example Question #1 : Simplifying Logarithms
Simplify the expression below.
Based on the definition of exponents, .
Then, we use the following rule of logarithms:
Thus, .
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