The definition of a logarithm is:
Master logarithm subtraction with same and different bases. Practice problems include step-by-step solutions using quotient rule and base change formula.
The definition of a logarithm is:
Where:
is the base of the exponent
is what appears inside the log, can also appear in parentheses
is the exponent we raise the log base to in order to obtain the number that appears inside of the log.
Subtraction of logarithms with different bases is performed by changing the base using the following rule:
Calculate the value of the following expression:
\( \ln4\times(\log_7x^7-\log_7x^4-\log_7x^3+\log_2y^4-\log_2y^3-\log_2y) \)
To solve the problem, we employ the property of logarithms for subtraction:
By applying the property, we simplify the expression to . This is equivalent to . Therefore:
Therefore, the result of the expression is .
Answer:
To solve the problem of evaluating , we apply the properties of logarithms as follows:
Thus, the simplified and evaluated result is .
Answer:
To solve the problem, let's use the rules of logarithms:
Therefore, the simplification results in the expression: .
This matches the correct answer from the given choices.
Answer:
To solve the problem , we need to apply the rules of logarithms:
Thus, the simplified expression is .
Using the provided answer choices, the correct answer matches choice , which corresponds to choice 2.
Therefore, the solution to the problem is .
Answer:
We break it down into parts
Answer: