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

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

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

simplify

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

2 ln (x) + ln (3 x - 2)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

= 2 ln (x) + ln (3 x - 2)

lo g_{3} (\frac{9}{x + 8})

lo g_{10} (a^{2}) + lo g_{10} (b) - lo g_{10} (a)

ln (7 x (cos (x))^{\frac{x}{2}})

lo g_{10} (a + b) - lo g_{10} (a) - lo g_{10} (b)

lo g_{10} (\frac{k}{r})

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