Condense the logarithmic expression $-\cos\left(x\right)\ln\left(\tan\left(x\right)+1\right)+\cos\left(x\right)\ln\left(\tan\left(x\right)-1\right)$

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  • Solve for x
  • Condense the logarithm
  • Expand the logarithm
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  • Write as single logarithm
  • Integrate by partial fractions
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Using the power rule of logarithms: $n\log_b(a)=\log_b(a^n)$, where $n$ equals $\cos\left(x\right)$

$-\ln\left(\left|\tan\left(x\right)+1\right|^{\cos\left(x\right)}\right)+\cos\left(x\right)\ln\left(\tan\left(x\right)-1\right)$

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$-\ln\left(\left|\tan\left(x\right)+1\right|^{\cos\left(x\right)}\right)+\cos\left(x\right)\ln\left(\tan\left(x\right)-1\right)$

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Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression -cos(x)ln(abs(tan(x)+1))+cos(x)ln(abs(tan(x)-1)). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals \cos\left(x\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals \cos\left(x\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n). Any expression to the power of 1 is equal to that same expression.

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Main Topic: Condensing Logarithms

Combining or condensing logarithms consists of rewriting a mathematical expression with several logarithms into a single logarithm, by applying the properties of logarithms.

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