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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

- \frac{6 ln ( \frac{9}{10} )}{ln ( 2 )}

ln (5) - ln (2) + 39

lo g_{10} (3) - lo g_{10} (7)

- lo g_{10} (1.34 \cdot 1 0^{- 5})

ln (x^{13} 5 - x)

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