What is ln(4x^6y^8) ?

The solution to ln(4x^6y^8) is 2ln(2)+6ln(x)+8ln(y)

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simplify ln(4x^6y^8)

simplify

ln (4 x^{6} y^{8})

2 ln (2) + 6 ln (x) + 8 ln (y)

Solution steps

ln (4 x^{6} y^{8})

Apply log rule:

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

ln (4 x^{6} y^{8}) = ln (4) + ln (x^{6}) + ln (y^{8})

= ln (4) + ln (x^{6}) + ln (y^{8})

Apply log rule:

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

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

= ln (4) + 6 ln (x) + ln (y^{8})

Apply log rule:

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

ln (y^{8}) = 8 ln (y)

= ln (4) + 6 ln (x) + 8 ln (y)

ln (4) = 2 ln (2)

= 2 ln (2) + 6 ln (x) + 8 ln (y)

- \frac{1}{π} ln (\frac{6}{2})

ln (\frac{3}{- 1})

0.15 \cdot lo g_{10} (1.31) + 0.65 \cdot lo g_{10} (\frac{45.57 + 176}{60})

lo g_{e} (\frac{x}{e})

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