What is expand ln(ln((x+1)^{cos(4x)})) ?

The solution to expand ln(ln((x+1)^{cos(4x)})) is ln(cos(4x))+ln(ln(x+1))

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expand ln(ln((x+1)^{cos(4x)}))

expand

ln (ln ((x + 1)^{c o s (4 x)}))

ln (cos (4 x)) + ln (ln (x + 1))

Solution steps

ln (ln ((x + 1)^{c o s (4 x)}))

Apply log rule:

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

ln ((x + 1)^{c o s (4 x)}) = cos (4 x) ln (x + 1)

= ln (cos (4 x) ln (x + 1))

Apply log rule:

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

ln (cos (4 x) ln (x + 1)) = ln (cos (4 x)) + ln (ln (x + 1))

= ln (cos (4 x) ln (x + 1))

Apply log rule:

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

ln (cos (4 x) ln (x + 1)) = ln (cos (4 x)) + ln (ln (x + 1))

= ln (cos (4 x)) + ln (ln (x + 1))

ln (x 1 + x^{2})

lo g_{10} (\frac{7 y}{9})

lo g_{5} (25 b)

3 ln (\frac{9}{2})

What is expand ln(ln((x+1)^{cos(4x)})) ?
The solution to expand ln(ln((x+1)^{cos(4x)})) is ln(cos(4x))+ln(ln(x+1))