What is join (7cos(7ln(x)))/x-sin(7ln(x)) ?

The solution to join (7cos(7ln(x)))/x-sin(7ln(x)) is (7cos(ln(x^7)))/x-sin(ln(x^7))

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join (7cos(7ln(x)))/x-sin(7ln(x))

join

\frac{7 cos ( 7 ln ( x ) )}{x} - sin (7 ln (x))

\frac{7 cos ( ln ( x ^{7} ) )}{x} - sin (ln (x^{7}))

Solution steps

\frac{7 cos ( 7 ln ( x ) )}{x} - sin (7 ln (x))

Apply log rule:

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

7 ln (x) = ln (x^{7})

= \frac{7 cos ( ln ( x ^{7} ) )}{x} - sin (7 ln (x))

Apply log rule:

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

7 ln (x) = ln (x^{7})

= \frac{7 cos ( ln ( x ^{7} ) )}{x} - sin (ln (x^{7}))

ln (\frac{2 x}{10})

- ln ∣ x - 3 ∣ + 2 ln ∣ x - 2 ∣ + c

\frac{ln ( \frac{3}{2} ) ln ( \frac{8}{7} )}{ln ( \frac{7}{6} )} + ln (\frac{1}{2})

\frac{1}{3} ln (\frac{11}{5})

ln (\frac{5 x}{6})

What is join (7cos(7ln(x)))/x-sin(7ln(x)) ?
The solution to join (7cos(7ln(x)))/x-sin(7ln(x)) is (7cos(ln(x^7)))/x-sin(ln(x^7))