What is sqrt(ln(x^4))+ln(1/x) ?

The solution to sqrt(ln(x^4))+ln(1/x) is sqrt(4ln(x))++ln(1)-ln(x)

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simplify sqrt(ln(x^4))+ln(1/x)

simplify

ln (x^{4}) + ln (\frac{1}{x})

4 ln (x) + + ln (1) - ln (x)

Solution steps

ln (x^{4}) + ln (\frac{1}{x})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

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

= ln (x^{4}) + + ln (1) - ln (x)

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

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

ln (\frac{( x - 3 )}{x + 2})

5 e^{l n (5) - l n (2)} - e^{2 (l n (5) - l n (2))}

ln (\frac{2 x}{y ^{2}})

lo g_{e} (\frac{∣ x + 1 ∣ - 1}{∣ x - 3 ∣ + 1})

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

What is sqrt(ln(x^4))+ln(1/x) ?
The solution to sqrt(ln(x^4))+ln(1/x) is sqrt(4ln(x))++ln(1)-ln(x)