What is 10ln(3x)-[ln(3x)]^2 ?

The solution to 10ln(3x)-[ln(3x)]^2 is 10ln(3)+10ln(x)-ln^2(3x)

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simplify 10ln(3x)-[ln(3x)]^2

simplify

10 ln (3 x) - [ln (3 x)]^{2}

10 ln (3) + 10 ln (x) - ln^{2} (3 x)

Solution steps

10 ln (3 x) - [ln (3 x)]^{2}

Apply log rule:

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

10 ln (3 x) = 10 ln (3) + 10 ln (x)

= 10 ln (3) + 10 ln (x) - [ln (3 x)]^{2}

Remove parentheses:

(a) = a

= 10 ln (3) + 10 ln (x) - ln^{2} (3 x)

ln (\frac{1}{θ} \cdot [1 - \frac{1}{θ}]^{x - 1})

ln (3 b \frac{b + 1}{b - 1})

5 ln (x) - \frac{1}{4} ln (y)

lo g_{4} (4 x^{2})

lo g_{4} (\frac{64}{x + 5})

What is 10ln(3x)-[ln(3x)]^2 ?
The solution to 10ln(3x)-[ln(3x)]^2 is 10ln(3)+10ln(x)-ln^2(3x)