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Exercise

$\ln\left(x^2e^2\right)$

Step-by-step Solution

1

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

$\ln\left(x^2\right)+\ln\left(e^2\right)$
2

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

$2\ln\left(x\right)+\ln\left(e^2\right)$
3

Calculating the natural logarithm of $e^2$

$2\ln\left(x\right)+2$
4

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

$2\ln\left(x\right)+2$

Final answer to the exercise

$2\ln\left(x\right)+2$

Try other ways to solve this exercise

  • Choose an option
  • 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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$\log\left(2x\right)$

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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