simplify ln(3x^6)

Solution

simplify

ln (3 x^{6})

ln (3) + 6 ln (x)

Solution steps

ln (3 x^{6})

Apply log rule:

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

ln (3 x^{6}) = ln (3) + ln (x^{6})

= ln (3) + ln (x^{6})

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= ln (3) + 6 ln (x)

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ln (\frac{1}{80})

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ln (\frac{1}{( 1 - x ^{2} )})