Question
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Tutor-Verified Answer
Answer
Solution
Certainly! Let’s simplify the expression
using logarithmic properties.
Given:
Objective:
Simplify the expression for
.
Steps:
-
Apply the Power Rule of Logarithms:The power rule states that
. Applying this to : -
Substitute Back into the Original Equation:
-
Simplify the Expression:Multiply the constants:
Final Simplified Form:
Summary:
By applying the power rule of logarithms, the original expression
simplifies to
.
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Extra Insights
To show that
, we can start by simplifying the right-hand side of the equation.
Using the logarithmic identity that states
, we have:
Now, substituting this back into our equation gives:
This can further be simplified to:
Thus, the expression simplifies to
.
However, the original request seems to suggest a transformation rather than an equality. Given the context and verifying through substitution or manipulation does not directly yield
as typically
will be defined as
through the simplification. Therefore, you may want to check the expression or the context from which
is derived.