simplify ln(5x^4y)

Solution

simplify

ln (5 x^{4} y)

ln (5) + 4 ln (x) + ln (y)

Solution steps

ln (5 x^{4} y)

Apply log rule:

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

ln (5 x^{4} y) = ln (5) + ln (x^{4}) + ln (y)

= ln (5) + ln (x^{4}) + ln (y)

Apply log rule:

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

ln (x^{4}) = 4 ln (x)

= ln (5) + 4 ln (x) + ln (y)

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