
If we are given the logarithmic equation and then
Answer
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Hint: First, we will understand what the logarithmic operator represents in mathematics. A logarithm function or log operator is used when we have to deal with the powers and base of a number, to understand it better which is
It’s basically a problem based on the logarithmic properties. We will mainly use two properties of the logarithm to solve this problem.
Formula used:
> Using the logarithm law,
> where n is any number that we can choose as the base of the log
Complete step-by-step solution:
Given that we have two logarithm values with the same base and even the required function needs the same base and so it is easy to solve with the log properties.
Since we have and . By using these two functions we need to find the value of
Let us convert the log function, by using multiplication.
And now then we have
Now by use of the property , then we get
Let (general algebraic expansion) substituting these values we get
Now using the properties and then we get
Since in the logarithm, same base value and functions get one which is then we get where
From the given that we have and substituting these values we get
Thus, we get
Therefore, the option is correct.
Note: The other more general properties of the logarithm are
where n is any number that we can choose as the base of the log
The log rules can be used for the fast exponent calculation using the multiplication operations. The most general base of the log is
It’s basically a problem based on the logarithmic properties. We will mainly use two properties of the logarithm to solve this problem.
Formula used:
> Using the logarithm law,
>
Complete step-by-step solution:
Given that we have two logarithm values with the same base
Since we have
Let us convert the log function,
And now
Now by use of the property
Let
Now using the properties
Since in the logarithm, same base value and functions get one which is
From the given that we have
Thus, we get
Therefore, the option
Note: The other more general properties of the logarithm are
The log rules can be used for the fast exponent calculation using the multiplication operations. The most general base of the log is
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