What is sqrt(ln^2(x)+3ln(x)) ?

The solution to sqrt(ln^2(x)+3ln(x)) is sqrt(ln^2(x^4))

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simplify sqrt(ln^2(x)+3ln(x))

simplify

ln^{2} (x) + 3 ln (x)

ln^{2} (x^{4})

Solution steps

ln^{2} (x) + 3 ln (x)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

3 ln (x) = ln (x^{3})

= ln^{2} (x) + ln (x^{3})

Apply log rule:

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

ln^{2} (x) + ln (x^{3}) = ln^{2} (x^{3} x)

= ln^{2} (x x^{3})

Simplify

x x^{3} : x^{4}

= ln^{2} (x^{4})

ln (b \cdot e^{- 2})

2 lo g_{6} (w - 2) - 3 lo g_{6} (w) + 9

ln (12) + 8 x + 5 - ln (3)

ln (4 e 4)

ln (\frac{2 ^{2}}{3 ( 4 ^{3} )})

What is sqrt(ln^2(x)+3ln(x)) ?
The solution to sqrt(ln^2(x)+3ln(x)) is sqrt(ln^2(x^4))