What is log_{a^{22a}}(-1/2 (log_{a}(2)+1)) ?

The solution to log_{a^{22a}}(-1/2 (log_{a}(2)+1)) is log_{a^{22a}}(log_{a}(2)+1)-log_{a^{22a}}(2)

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simplify log_{a^{22a}}(-1/2 (log_{a}(2)+1))

simplify

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1))

lo g_{a^{22 a}} (lo g_{a} (2) + 1) - lo g_{a^{22 a}} (2)

Solution steps

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1))

Apply log rule:

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

lo g_{a^{22 a}} (- \frac{1}{2} (lo g_{a} (2) + 1)) = lo g_{a^{22 a}} (\frac{1}{2}) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

= lo g_{a^{22 a}} (\frac{1}{2}) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

Apply log rule:

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

lo g_{a^{22 a}} (\frac{1}{2}) = lo g_{a^{22 a}} (1) - lo g_{a^{22 a}} (2)

= lo g_{a^{22 a}} (1) - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

Apply log rule:

lo g_{a} (1) = 0

= 0 - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

0 - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1) = - lo g_{a^{22 a}} (2) + lo g_{a^{22 a}} (lo g_{a} (2) + 1)

= lo g_{a^{22 a}} (lo g_{a} (2) + 1) - lo g_{a^{22 a}} (2)

ln (10 x e^{\frac{- x}{50}})

lo g_{10} (\frac{3 x ^{2} - 15 x}{x ^{2} + 4 x})

ln (\frac{12 x ^{5}}{y})

50 \cdot ln (\frac{54.8}{29.5})

ln (\frac{1}{x}) - ln (\frac{2}{x})

What is log_{a^{22a}}(-1/2 (log_{a}(2)+1)) ?
The solution to log_{a^{22a}}(-1/2 (log_{a}(2)+1)) is log_{a^{22a}}(log_{a}(2)+1)-log_{a^{22a}}(2)