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Popular >

simplify ln((x^4)/(e^{3y)})

Solution

simplify

ln (\frac{x ^{4}}{e ^{3 y}})

Solution

4 ln (x) - 3 y

Solution steps

ln (\frac{x ^{4}}{e ^{3 y}})

Apply log rule:

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

ln (\frac{x ^{4}}{e ^{3 y}}) = ln (x^{4}) - ln (e^{3 y})

= ln (x^{4}) - ln (e^{3 y})

Apply log rule:

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

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

= 4 ln (x) - ln (e^{3 y})

Apply log rule:

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

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

= 4 ln (x) - 3 y ln (e)

3 y ln (e) = 3 y

= 4 ln (x) - 3 y

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Frequently Asked Questions (FAQ)

What is ln((x^4)/(e^{3y)}) ?
The solution to ln((x^4)/(e^{3y)}) is 4ln(x)-3y