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Popular >

simplify 4ln(xy)+ln(y)-ln(x^4y)

Solution

simplify

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

Solution

ln (y^{4})

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

Simplify

(x y)^{4} y : x^{4} y^{5}

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{4} y^{5}) - ln (x^{4} y) = ln (\frac{x ^{4} y ^{5}}{x ^{4} y})

= ln (\frac{x ^{4} y ^{5}}{x ^{4} y})

Simplify

\frac{x ^{4} y ^{5}}{x ^{4} y} : y^{4}

= ln (y^{4})

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Frequently Asked Questions (FAQ)

What is 4ln(xy)+ln(y)-ln(x^4y) ?
The solution to 4ln(xy)+ln(y)-ln(x^4y) is ln(y^4)