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Popular >

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

Solution

simplify

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

Solution

3 x + 3 ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

3 x ln (e) = 3 x

= 3 x + 3 ln (y)

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Frequently Asked Questions (FAQ)

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