What is ln(e^5xe^2) ?

The solution to ln(e^5xe^2) is ln(x)+7

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simplify ln(e^5xe^2)

simplify

ln (e^{5} x e^{2})

ln (x) + 7

Solution steps

ln (e^{5} x e^{2})

Apply log rule:

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

ln (e^{5} x e^{2}) = ln (e^{5}) + ln (x) + ln (e^{2})

= ln (e^{5}) + ln (x) + ln (e^{2})

Apply log rule:

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

ln (e^{5}) = 5 ln (e)

= 5 ln (e) + ln (x) + ln (e^{2})

Apply log rule:

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

ln (e^{2}) = 2 ln (e)

= 5 ln (e) + ln (x) + 2 ln (e)

Group like terms

= ln (x) + 5 ln (e) + 2 ln (e)

Add similar elements:

5 ln (e) + 2 ln (e) = 7 ln (e)

= ln (x) + 7 ln (e)

7 ln (e) = 7

= ln (x) + 7

ln (αx e^{β x})

- lo g_{10} (2.56 \cdot 1 0^{- 11})

2 ln (x + 3) + 2 ln (x - 3) + c

9 lo g_{135} (- 9 lo g_{5} (x))

ln (\frac{x ^{2} - 9}{x ^{3} + 27})