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Simplify e^(ln 12-ln 6) and write without any logarithms. Answer:

Simplify eln⁡12−ln⁡6 e^{\ln 12-\ln 6} and write without any logarithms.\newlineAnswer:

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Full solution

Q. Simplify eln⁡12−ln⁡6 e^{\ln 12-\ln 6} and write without any logarithms.\newlineAnswer:
  1. Apply Logarithm Properties: Apply the properties of logarithms to simplify the expression inside the exponent. The difference of logarithms ln⁡(a)−ln⁡(b)\ln(a) - \ln(b) is equivalent to the logarithm of the division of aa by bb, which is ln⁡(ab)\ln(\frac{a}{b}). So, e(ln⁡12−ln⁡6)e^{(\ln 12 - \ln 6)} becomes e(ln⁡(126))e^{(\ln(\frac{12}{6}))}.
  2. Simplify Fraction: Simplify the fraction inside the logarithm. \newline1212 divided by 66 equals 22, so eln⁡(126)e^{\ln(\frac{12}{6})} simplifies to eln⁡2e^{\ln 2}.
  3. Apply Exponential Property: Apply the property of logarithms and exponents that eln⁡x=xe^{\ln x} = x. Since ee and ln⁡\ln are inverse functions, eln⁡2e^{\ln 2} simplifies to just 22.

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