What is log_{4}(16(x^2-49)) ?

The solution to log_{4}(16(x^2-49)) is 2+log_{4}(x^2-49)

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simplify log_{4}(16(x^2-49))

simplify

lo g_{4} (16 (x^{2} - 49))

2 + lo g_{4} (x^{2} - 49)

Solution steps

lo g_{4} (16 (x^{2} - 49))

Factor the number:

16 = 4^{2}

= lo g_{4} (4^{2} (x^{2} - 49))

Apply log rule:

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

lo g_{4} (4^{2} (x^{2} - 49)) = lo g_{4} (4^{2}) + lo g_{4} (x^{2} - 49)

= lo g_{4} (4^{2}) + lo g_{4} (x^{2} - 49)

Apply log rule:

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

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

= 2 + lo g_{4} (x^{2} - 49)

lo g_{10} (ab c)

ln (- 5 x)

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

2 ln (x) + 5 ln (x - 2)

\frac{1}{2} ln (\frac{6}{1 - e ^{- 6}})

What is log_{4}(16(x^2-49)) ?
The solution to log_{4}(16(x^2-49)) is 2+log_{4}(x^2-49)