What is ln(e^{19}x^{20}) ?

The solution to ln(e^{19}x^{20}) is 19+20ln(x)

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simplify ln(e^{19}x^{20})

simplify

ln (e^{19} x^{20})

19 + 20 ln (x)

Solution steps

ln (e^{19} x^{20})

Apply log rule:

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

ln (e^{19} x^{20}) = ln (e^{19}) + ln (x^{20})

= ln (e^{19}) + ln (x^{20})

Apply log rule:

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

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

= 19 ln (e) + ln (x^{20})

Apply log rule:

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

ln (x^{20}) = 20 ln (x)

= 19 ln (e) + 20 ln (x)

19 ln (e) = 19

= 19 + 20 ln (x)

lo g_{10} (\frac{x ^{3} ( x + 3 )}{( x - 1 ) x + 5})

\frac{2 ln ( 2 )}{ln ( 2 ) - 2 ln ( 3 )}

- \frac{1}{ln ( 10 ) 0.5 \cdot lo g _{10} ( 0. 5 ^{2} )} - \frac{7}{( 0 , 5 + 3 ) ^{3}}

lo g_{3} (\frac{m}{n})

lo g_{b} (ab)