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Simplify e^(ln 10-ln 8) and write without any logarithms. Answer:

Simplify eln⁡10−ln⁡8 e^{\ln 10-\ln 8} and write without any logarithms.\newlineAnswer:

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Simplify eln⁡10−ln⁡8 e^{\ln 10-\ln 8} and write without any logarithms.\newlineAnswer:
  1. Apply Logarithm Property: Apply the property of logarithms that states ln⁡(a)−ln⁡(b)=ln⁡(ab)\ln(a) - \ln(b) = \ln\left(\frac{a}{b}\right).eln⁡10−ln⁡8=eln⁡(108)e^{\ln 10 - \ln 8} = e^{\ln(\frac{10}{8})}
  2. Simplify Fraction: Simplify the fraction inside the logarithm.\newlineeln⁡(108)=eln⁡(54)e^{\ln(\frac{10}{8})} = e^{\ln(\frac{5}{4})}
  3. Apply Exponent Property: Apply the property of exponents and logarithms that states eln⁡x=xe^{\ln x} = x.eln⁡(54)=54e^{\ln(\frac{5}{4})} = \frac{5}{4}

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