simplify ln(31x^5y)

Solution

simplify

ln (31 x^{5} y)

ln (31) + 5 ln (x) + ln (y)

Solution steps

ln (31 x^{5} y)

Apply log rule:

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

ln (31 x^{5} y) = ln (31) + ln (x^{5}) + ln (y)

= ln (31) + ln (x^{5}) + ln (y)

Apply log rule:

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

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

= ln (31) + 5 ln (x) + ln (y)

lo g_{2} (6) + lo g_{2} (12)

lo g_{10} (\frac{x}{y ^{9} z ^{5}})

lo g_{4} (11) - lo g_{4} (9)

4 ln (3 x) - ln (9 x)

lo g_{10} (z \cdot w x \cdot y)