What is log_{2}(16x^7) ?

The solution to log_{2}(16x^7) is 4+7log_{2}(x)

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simplify log_{2}(16x^7)

simplify

lo g_{2} (16 x^{7})

4 + 7 lo g_{2} (x)

Solution steps

lo g_{2} (16 x^{7})

Factor the number:

16 = 2^{4}

= lo g_{2} (2^{4} x^{7})

Apply log rule:

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

lo g_{2} (2^{4} x^{7}) = lo g_{2} (2^{4}) + lo g_{2} (x^{7})

= lo g_{2} (2^{4}) + lo g_{2} (x^{7})

Apply log rule:

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

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

= 4 + lo g_{2} (x^{7})

Apply log rule

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

lo g_{2} (x^{7}) = 7 lo g_{2} (x)

= 4 + 7 lo g_{2} (x)

lo g_{10} (\frac{3 b}{c})

\frac{1}{2} lo g_{2 (x)} (+ 2 lo g_{10} (2) (x - 6))

\frac{1}{3} ln (x) + 4 ln (\frac{( x - 3 ) ( x + 3 ) ^{\frac{5}{8}}}{x + 3})

4 lo g_{4} (2) + 2 lo g_{4} (7)

lo g_{10} (\frac{s}{( s - 1 )})