Math  /  Algebra

QuestionUse the properties of logarithms to simplify the expression ln(sinθ)ln(sinθ4)\ln (\sin \theta)-\ln \left(\frac{\sin \theta}{4}\right). ln(sinθ)ln(sinθ4)=\ln (\sin \theta)-\ln \left(\frac{\sin \theta}{4}\right)=\square (Type an exact answer.)

Studdy Solution
Simplify the expression inside the logarithm:
sinθsinθ4=sinθ×4sinθ=4 \frac{\sin \theta}{\frac{\sin \theta}{4}} = \frac{\sin \theta \times 4}{\sin \theta} = 4
Thus, the expression simplifies to:
ln(4) \ln(4)
The simplified expression is:
ln(4) \boxed{\ln(4)}

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