What is log_{10}((e^2)/4) ?

The solution to log_{10}((e^2)/4) is 2log_{10}(e)-2log_{10}(2)

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simplify log_{10}((e^2)/4)

simplify

lo g_{10} (\frac{e ^{2}}{4})

2 lo g_{10} (e) - 2 lo g_{10} (2)

Solution steps

lo g_{10} (\frac{e ^{2}}{4})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{10} (\frac{e ^{2}}{4}) = lo g_{10} (e^{2}) - lo g_{10} (4)

= lo g_{10} (e^{2}) - lo g_{10} (4)

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

lo g_{10} (e^{2}) = 2 lo g_{10} (e)

= 2 lo g_{10} (e) - lo g_{10} (4)

lo g_{10} (4) = 2 lo g_{10} (2)

= 2 lo g_{10} (e) - 2 lo g_{10} (2)

ln (\frac{102}{760})

ln (1 + 0.999) - ln (0.999)

ln (0.1 + 0.5) - ln (0.5)

ln (\frac{2 \cdot 3}{3})

ln (\frac{51.104}{47.2})

What is log_{10}((e^2)/4) ?
The solution to log_{10}((e^2)/4) is 2log_{10}(e)-2log_{10}(2)