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Popular >

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

Solution

simplify

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

Solution

19 ln (x) + 17 x

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

17 x ln (e) = 17 x

= 19 ln (x) + 17 x

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Frequently Asked Questions (FAQ)

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