Respuesta :
The solution for the given logarithmic expression log₂4+3 log₂9 as a single logarithm is log₂ (2916).
What are the logarithmic expression?
A logarithmic equation is one that includes a logarithm in the variable x.
An exponential formula is one where the variable is represented by an exponent. To answer exponential equations, first determine whether both sides of the equation can be written as powers of the exact number. If you can't, take the common logarithm from both of the equation's sides and use property 7 to solve the problem.
- Quotient Rule: ㏒(A/B) = ㏒A - ㏒B
- Product Rule : ㏒A + ㏒B = ㏒(AB)
- Power Rule: n㏒A = ㏒Aⁿ
Now, as per the stated condition in question;
The expressed equation is;
= log₂4+3 log₂9
Using the Power Rule in the second term.
= log₂4+log₂9³
= log₂4+log₂729
As, the base of each log term is 2. We can use product rule to simplify the equation.
= log₂(4×729)
= log₂ (2916) [As a single log function]
Therefore, the simplification of the given logarithmic expression as the single logarithm is log₂ (2916).
To know more about the logarithmic expression, here
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