What is log_{4}(1e^{20}) ?

The solution to log_{4}(1e^{20}) is 20log_{4}(e)

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simplify log_{4}(1e^{20})

simplify

lo g_{4} (1 e^{20})

20 lo g_{4} (e)

Decimal Notation

14.42695 \dots

Solution steps

lo g_{4} (1 \cdot e^{20})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{4} (1 \cdot e^{20}) = lo g_{4} (1) + lo g_{4} (e^{20})

= lo g_{4} (1) + lo g_{4} (e^{20})

Apply log rule:

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

lo g_{4} (e^{20}) = 20 lo g_{4} (e)

= lo g_{4} (1) + 20 lo g_{4} (e)

Apply log rule:

lo g_{a} (1) = 0

= 0 + 20 lo g_{4} (e)

0 + 20 lo g_{4} (e) = 20 lo g_{4} (e)

= 20 lo g_{4} (e)

\frac{d}{d x} (\frac{1}{x ^{2} + 1}) + ln (\frac{1}{x})

\frac{7}{30} (ln (7) - ln (2))

lo g_{2} (x - 3) + lo g_{2} (x - 1)

ln (2) e^{- 6} + (- 2.268) \cdot ln (0.15)

lo g_{10} (525) 5