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Popular >

simplify ln(x^{17}e^{19x})

Solution

simplify

ln (x^{17} e^{19 x})

Solution

17 ln (x) + 19 x

Solution steps

ln (x^{17} e^{19 x})

Apply log rule:

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

ln (x^{17} e^{19 x}) = ln (x^{17}) + ln (e^{19 x})

= ln (x^{17}) + ln (e^{19 x})

Apply log rule:

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

ln (x^{17}) = 17 ln (x)

= 17 ln (x) + ln (e^{19 x})

Apply log rule:

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

ln (e^{19 x}) = 19 x ln (e)

= 17 ln (x) + 19 x ln (e)

19 x ln (e) = 19 x

= 17 ln (x) + 19 x

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Frequently Asked Questions (FAQ)

What is ln(x^{17}e^{19x}) ?
The solution to ln(x^{17}e^{19x}) is 17ln(x)+19x