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Exercise

log(log(2x+3))−(log(log(x−5)))log\left(log\left(2x+3\right)\right)-\left(log\left(log\left(x-5\right)\right)\right)

Step-by-step Solution

1

The difference of two logarithms of equal base bb is equal to the logarithm of the quotient: log⁡b(x)−log⁡b(y)=log⁡b(xy)\log_b(x)-\log_b(y)=\log_b\left(\frac{x}{y}\right)

log⁡(log⁡(2x+3)log⁡(x−5))\log \left(\frac{\log \left(2x+3\right)}{\log \left(x-5\right)}\right)

Final answer to the exercise

log⁡(log⁡(2x+3)log⁡(x−5))\log \left(\frac{\log \left(2x+3\right)}{\log \left(x-5\right)}\right)

Try other ways to solve this exercise

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  • Solve for x
  • Condense the logarithm
  • Expand the logarithm
  • Simplify
  • Find the integral
  • Find the derivative
  • Write as single logarithm
  • Integrate by partial fractions
  • Product of Binomials with Common Term
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log(log(2x+3))−(log(log(x−5)))
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