What is expand ln((1+sin(2x))^{cos(x)}) ?

The solution to expand ln((1+sin(2x))^{cos(x)}) is cos(x)ln(1+sin(2x))

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expand ln((1+sin(2x))^{cos(x)})

expand

ln ((1 + sin (2 x))^{c o s (x)})

cos (x) ln (1 + sin (2 x))

Solution steps

ln ((1 + sin (2 x))^{c o s (x)})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((1 + sin (2 x))^{c o s (x)}) = cos (x) ln (1 + sin (2 x))

= cos (x) ln (1 + sin (2 x))

ln (\frac{e ^{2}}{1 + e ^{2}})

- y + ln (x y) + x ln (x)

\frac{4}{5} lo g_{3} (80)

ln (\frac{3 x ^{2} ( 1 - x )}{16})

lo g_{10} (\frac{sin ( x )}{x})

What is expand ln((1+sin(2x))^{cos(x)}) ?
The solution to expand ln((1+sin(2x))^{cos(x)}) is cos(x)ln(1+sin(2x))