What is log_{2}(4x^3) ?

The solution to log_{2}(4x^3) is 2+3log_{2}(x)

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simplify log_{2}(4x^3)

simplify

lo g_{2} (4 x^{3})

2 + 3 lo g_{2} (x)

Solution steps

lo g_{2} (4 x^{3})

Factor the number:

4 = 2^{2}

= lo g_{2} (2^{2} x^{3})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{2} (2^{2} x^{3}) = lo g_{2} (2^{2}) + lo g_{2} (x^{3})

= lo g_{2} (2^{2}) + lo g_{2} (x^{3})

Apply log rule:

lo g_{a} (a^{b}) = b

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

= 2 + lo g_{2} (x^{3})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{2} (x^{3}) = 3 lo g_{2} (x)

= 2 + 3 lo g_{2} (x)

- lo g_{10} (4.3 \cdot 1 0^{- 5})

lo g_{5} (11) + lo g_{5} (8)

lo g_{4} (\frac{35}{5}) + lo g_{4} (\frac{10}{9})

lo g_{5} (\frac{25 b ^{5} y ^{2} - 8}{y ( x + 8 ) ^{2}})

ln (\frac{x + h}{x})