What is ln(x^2sqrt(3x^2-1)) ?

The solution to ln(x^2sqrt(3x^2-1)) is 2ln(x)+ln(sqrt(3x^2-1))

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simplify ln(x^2sqrt(3x^2-1))

simplify

ln (x^{2} 3 x^{2} - 1)

2 ln (x) + ln (3 x^{2} - 1)

Solution steps

ln (x^{2} 3 x^{2} - 1)

Apply log rule:

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

ln (x^{2} 3 x^{2} - 1) = ln (x^{2}) + ln (3 x^{2} - 1)

= ln (x^{2}) + ln (3 x^{2} - 1)

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} - 1)

- lo g_{10} (5.011 \cdot 1 0^{- 5})

ln (\frac{1}{49})

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

What is ln(x^2sqrt(3x^2-1)) ?
The solution to ln(x^2sqrt(3x^2-1)) is 2ln(x)+ln(sqrt(3x^2-1))