What is log_{2}((2a^3)/b) ?

The solution to log_{2}((2a^3)/b) is 1+3log_{2}(a)-log_{2}(b)

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simplify log_{2}((2a^3)/b)

simplify

lo g_{2} (\frac{2 a ^{3}}{b})

1 + 3 lo g_{2} (a) - lo g_{2} (b)

Solution steps

lo g_{2} (\frac{2 a ^{3}}{b})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{2 a ^{3}}{b}) = lo g_{2} (2 a^{3}) - lo g_{2} (b)

= lo g_{2} (2 a^{3}) - lo g_{2} (b)

Simplify

lo g_{2} (2 a^{3}) : 1 + 3 lo g_{2} (a)

= 1 + 3 lo g_{2} (a) - lo g_{2} (b)

\frac{1}{2} lo g_{a} (8 x^{2}) - \frac{1}{6} lo g_{a} (8 x^{3})

lo g_{3} (\frac{2 x}{y})

ln (\frac{( 6 x - 4 ) ( 2 y )}{3 x})

lo g_{9} (4) - lo g_{9} (2) + 2 lo g_{9} (5)

lo g_{9} (4) - lo g_{9} (5)

What is log_{2}((2a^3)/b) ?
The solution to log_{2}((2a^3)/b) is 1+3log_{2}(a)-log_{2}(b)