What is ln(3x^4(sqrt(y^2-3))^3) ?

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

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simplify ln(3x^4(sqrt(y^2-3))^3)

simplify

ln (3 x^{4} (y^{2} - 3)^{3})

ln (3) + 4 ln (x) + 3 ln (y^{2} - 3)

Solution steps

ln (3 x^{4} (y^{2} - 3)^{3})

Apply log rule:

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

ln (3 x^{4} (y^{2} - 3)^{3}) = ln (3) + ln (x^{4}) + ln ((y^{2} - 3)^{3})

= ln (3) + ln (x^{4}) + ln ((y^{2} - 3)^{3})

Apply log rule:

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

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

= ln (3) + 4 ln (x) + ln ((y^{2} - 3)^{3})

Apply log rule:

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

ln ((y^{2} - 3)^{3}) = 3 ln (y^{2} - 3)

= ln (3) + 4 ln (x) + 3 ln (y^{2} - 3)

\frac{4}{3 ln ( 3 )} + \frac{10}{3} - \frac{2}{ln ( 2 )}

2 \cdot ln (x) + \frac{1}{3} \cdot ln (x - 2) - 5 \cdot ln (2 x + 3)

ln (3) - ln (3 - x)

27 lo g_{10} (x) + lo g_{10} (y) - 12 lo g_{10} (z)

ln (0.42) + ln (0.37) + ln (0.64) + ln (0.55)

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