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Simplify e^(ln 6-ln 3) and write without any logarithms. Answer:

Simplify eln⁡6−ln⁡3 e^{\ln 6-\ln 3} and write without any logarithms.\newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Simplify eln⁡6−ln⁡3 e^{\ln 6-\ln 3} and write without any logarithms.\newlineAnswer:
  1. Apply logarithmic property: Use the property of logarithms that ln⁡(a)−ln⁡(b)=ln⁡(ab)\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right). \newlinee(ln⁡6−ln⁡3)=eln⁡(63)e^{(\ln 6 - \ln 3)} = e^{\ln(\frac{6}{3})}
  2. Simplify fraction: Simplify the fraction inside the logarithm.\newlineeln⁡(63)=eln⁡(2)e^{\ln(\frac{6}{3})} = e^{\ln(2)}
  3. Apply exponential property: Apply the property that eln⁡x=xe^{\ln x} = x for any x > 0.\newlineeln⁡(2)=2e^{\ln(2)} = 2

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