What is log_{4}(2(8x^6)) ?

The solution to log_{4}(2(8x^6)) is 6log_{4}(x)+2

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simplify log_{4}(2(8x^6))

simplify

lo g_{4} (2 (8 x^{6}))

6 lo g_{4} (x) + 2

Solution steps

lo g_{4} (2 (8 x^{6}))

Apply log rule:

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

lo g_{4} (2 (8 x^{6})) = lo g_{4} (2) + lo g_{4} (8 x^{6})

= lo g_{4} (2) + lo g_{4} (8 x^{6})

lo g_{4} (2) = \frac{1}{2}

lo g_{4} (8 x^{6}) = \frac{12 lo g _{4} ( x ) + 3}{2}

= \frac{1}{2} + \frac{12 lo g _{4} ( x ) + 3}{2}

Join

\frac{1}{2} + \frac{12 lo g _{4} ( x ) + 3}{2} : \frac{12 lo g _{4} ( x ) + 4}{2}

= \frac{12 lo g _{4} ( x ) + 4}{2}

Factor out common term

4 : 4 (3 lo g_{4} (x) + 1)

= \frac{4 ( 3 lo g _{4} ( x ) + 1 )}{2}

Divide the numbers:

\frac{4}{2} = 2

= 2 (3 lo g_{4} (x) + 1)

Expand

2 (3 lo g_{4} (x) + 1) : 6 lo g_{4} (x) + 2

= 6 lo g_{4} (x) + 2

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

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)