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

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

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

simplify

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

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

Solution steps

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

Factor the number:

16 = 2^{4}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (\frac{2}{25})

lo g_{x^{5}} (2 x^{2})

lo g_{3} (9 x^{4})

ln (x^{2} - 3 x - 4) - ln (x - 4) + ln (x + 1)

lo g_{4} (13 b^{2} c)

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