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Popular >

simplify ln((e^xy^3)/x)

Solution

simplify

ln (\frac{e ^{x} y ^{3}}{x})

Solution

x + 3 ln (y) - ln (x)

Solution steps

ln (\frac{e ^{x} y ^{3}}{x})

Apply log rule:

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

ln (\frac{e ^{x} y ^{3}}{x}) = ln (e^{x} y^{3}) - ln (x)

= ln (e^{x} y^{3}) - ln (x)

Apply log rule:

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

ln (e^{x} y^{3}) = ln (e^{x}) + ln (y^{3})

= ln (e^{x}) + ln (y^{3}) - ln (x)

Apply log rule:

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

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

= x ln (e) + ln (y^{3}) - ln (x)

Apply log rule:

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

ln (y^{3}) = 3 ln (y)

= x ln (e) + 3 ln (y) - ln (x)

x ln (e) = x

= x + 3 ln (y) - ln (x)

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Frequently Asked Questions (FAQ)

What is ln((e^xy^3)/x) ?
The solution to ln((e^xy^3)/x) is x+3ln(y)-ln(x)