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ExtremeBDS [4]
2 years ago
10

Expanding logarithmic Expression In Exercise,Use the properties of logarithms to rewrite the expression as a sum,difference,or m

ultipal of logarithms.See example 3.
In 2x/(x^2 - 1)1/2
Mathematics
1 answer:
wel2 years ago
6 0

Answer:

\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)

Step-by-step explanation:

In 2x/(x^2 - 1)1/2

ln(\frac{2x}{x^2-1} )^\frac{1}{2}

Apply the property of natural log

ln x^m = m ln(x) move the exponent before ln

ln(\frac{2x}{x^2-1} )^\frac{1}{2}

\frac{1}{2}ln(\frac{2x}{x^2-1})

ln(m/n)= ln m - ln n

\frac{1}{2}(ln(2x)-ln(x^2-1))

multiply 1/2 inside the terms

\frac{1}{2}ln(2x)-\frac{1}{2}ln(x^2-1)

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