What is expand ln^x(x)(ln(ln(x))+1/(ln(x))) ?

The solution to expand ln^x(x)(ln(ln(x))+1/(ln(x))) is ln(ln(x))ln^x(x)+ln^{x-1}(x)

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expand ln^x(x)(ln(ln(x))+1/(ln(x)))

expand

ln^{x} (x) (ln (ln (x)) + \frac{1}{ln ( x )})

ln (ln (x)) ln^{x} (x) + ln^{x - 1} (x)

Solution steps

ln^{x} (x) (ln (ln (x)) + \frac{1}{ln ( x )})

Apply the distributive law:

a (b + c) = ab + a c

a = ln^{x} (x), b = ln (ln (x)), c = \frac{1}{ln ( x )}

= ln^{x} (x) ln (ln (x)) + ln^{x} (x) \frac{1}{ln ( x )}

= ln^{x} (x) ln (ln (x)) + \frac{1}{ln ( x )} ln^{x} (x)

\frac{1}{ln ( x )} ln^{x} (x) = ln^{x - 1} (x)

= ln (ln (x)) ln^{x} (x) + ln^{x - 1} (x)

\frac{2 s + 1}{s ( s + 2 ) ( s - 1 )}

\frac{2 x ^{2} + 11 x + m}{( 2 x + 3 ) ( x - 5 )}

\frac{s + 2}{( s ^{2} + 3 s + 5 ) ( s + 1 )}

\frac{100}{s ( 0.5 s + 1 )} + \frac{10}{0.5 s + 1}

- 12 (- 10 x^{2} - 13 x + 13)^{2}

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