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Exercise

$\ln\sqrt{ab}$

Step-by-step Solution

1

Using the power rule of logarithms: $\log_a(x^n)=n\cdot\log_a(x)$

$\frac{1}{2}\ln\left(ab\right)$
2

Applying the product rule for logarithms: $\log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right)$

$\frac{1}{2}\left(\ln\left(a\right)+\ln\left(b\right)\right)$
3

Multiply the single term $\frac{1}{2}$ by each term of the polynomial $\left(\ln\left(a\right)+\ln\left(b\right)\right)$

$\frac{1}{2}\ln\left(a\right)+\frac{1}{2}\ln\left(b\right)$

Final answer to the exercise

$\frac{1}{2}\ln\left(a\right)+\frac{1}{2}\ln\left(b\right)$

Try other ways to solve this exercise

  • Choose an option
  • 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
  • FOIL Method
  • Load more...
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Similar Questions Solved

$\log_3\left(\frac{1}{81}\right)$

$\log\left(10x^5\right)$

$\log_3\left(2x\right)$

$\log_4\left(\frac{1}{64}\right)$

$\log_3\left(x^2\right)$

$\ln\left(3x\right)$

$\log\left(2x\right)$

Main Topic: Expanding Logarithms

Logarithm expansion consists of applying the properties of logarithms to express a single logarithm in multiple logarithms, usually much simpler.

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