Simplify/Condense log of (3x^2)/12

Problem

(log_)((3*x2)/12)

Solution

1. Simplify the fraction inside the logarithm by dividing both the numerator and the denominator by their greatest common factor, which is 3

(3*x2)/12=(x2)/4

2. Substitute the simplified fraction back into the logarithmic expression.

(log_)((x2)/4)

3. Apply the quotient rule for logarithms, (log_)(a/b)=(log_)(a)−(log_)(b) to separate the terms.

(log_)(x2)−(log_)(4)

4. Apply the power rule for logarithms, (log_)(an)=n*(log_)(a) to the first term and rewrite the second term if desired.

2*(log_)(x)−(log_)(4)

Final Answer

(log_)((3*x2)/12)=(log_)((x2)/4)

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