What is ln(cos(2x)(x+4)/x) ?

The solution to ln(cos(2x)(x+4)/x) is ln(cos(2x))++ln(x+4)-ln(x)

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simplify ln(cos(2x)(x+4)/x)

simplify

ln (cos (2 x) \frac{x + 4}{x})

ln (cos (2 x)) + + ln (x + 4) - ln (x)

Solution steps

ln (cos (2 x) \frac{x + 4}{x})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (cos (2 x) \frac{x + 4}{x}) = ln (cos (2 x)) + ln (\frac{x + 4}{x})

= ln (cos (2 x)) + ln (\frac{x + 4}{x})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{x + 4}{x}) = ln (x + 4) - ln (x)

= ln (cos (2 x)) + + ln (x + 4) - ln (x)

ln (4) - ln (9 - 4)

- ln (5.4 - 3) + 2 ln (5.4 - 2) + c

ln (3) + 3 ln (2)

182000 (ln (0.41) - ln (1.3))

\frac{1}{4} lo g_{4} (y) - \frac{1}{2} lo g_{4} (x)

What is ln(cos(2x)(x+4)/x) ?
The solution to ln(cos(2x)(x+4)/x) is ln(cos(2x))++ln(x+4)-ln(x)