simplify ln(y^5x^6)

Solution

simplify

ln (y^{5} x^{6})

5 ln (y) + 6 ln (x)

Solution steps

ln (y^{5} x^{6})

Apply log rule:

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

ln (y^{5} x^{6}) = ln (y^{5}) + ln (x^{6})

= ln (y^{5}) + ln (x^{6})

Apply log rule:

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

ln (y^{5}) = 5 ln (y)

= 5 ln (y) + ln (x^{6})

Apply log rule:

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

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

= 5 ln (y) + 6 ln (x)

- lo g_{10} (1.64 \cdot 1 0^{- 2})

ln (x + 5) + ln (2)

3.47 + lo g_{10} (\frac{0.8}{0.25})

ln (- \frac{1}{6} e^{3 x})

lo g_{10}^{2} (x) + lo g_{10} (x) - 2