What is expand ln(ln((sinh(x)+cosh(x))^2)) ?

The solution to expand ln(ln((sinh(x)+cosh(x))^2)) is ln(2)+ln(ln(sinh(x)+cosh(x)))

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expand ln(ln((sinh(x)+cosh(x))^2))

expand

ln (ln ((sinh (x) + cosh (x))^{2}))

ln (2) + ln (ln (sinh (x) + cosh (x)))

Solution steps

ln (ln ((sinh (x) + cosh (x))^{2}))

Apply log rule:

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

ln ((sinh (x) + cosh (x))^{2}) = 2 ln (sinh (x) + cosh (x))

= ln (2 ln (sinh (x) + cosh (x)))

Apply log rule:

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

ln (2 ln (sinh (x) + cosh (x))) = ln (2) + ln (ln (sinh (x) + cosh (x)))

= ln (2 ln (sinh (x) + cosh (x)))

Apply log rule:

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

ln (2 ln (sinh (x) + cosh (x))) = ln (2) + ln (ln (sinh (x) + cosh (x)))

= ln (2) + ln (ln (sinh (x) + cosh (x)))

ln (\frac{19}{3})

2 lo g_{6} (x) - 3 lo g_{6} (y)

5 ln (x) + 6 ln (y)

lo g_{10} (\frac{7 x ( 2 - x )}{2 ( x - 1 ) ^{3}})

ln (\frac{1000000}{415382})

What is expand ln(ln((sinh(x)+cosh(x))^2)) ?
The solution to expand ln(ln((sinh(x)+cosh(x))^2)) is ln(2)+ln(ln(sinh(x)+cosh(x)))