What is ln(3e^{7x^2-13x+5}) ?

The solution to ln(3e^{7x^2-13x+5}) is ln(3)+7x^2-13x+5

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simplify ln(3e^{7x^2-13x+5})

simplify

ln (3 e^{7 x^{2} - 13 x + 5})

ln (3) + 7 x^{2} - 13 x + 5

Solution steps

ln (3 e^{7 x^{2} - 13 x + 5})

Apply log rule:

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

ln (3 e^{7 x^{2} - 13 x + 5}) = ln (3) + ln (e^{7 x^{2} - 13 x + 5})

= ln (3) + ln (e^{7 x^{2} - 13 x + 5})

Apply log rule:

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

ln (e^{7 x^{2} - 13 x + 5}) = (7 x^{2} - 13 x + 5) ln (e)

= ln (3) + (7 x^{2} - 13 x + 5) ln (e)

(7 x^{2} - 13 x + 5) ln (e) = 7 x^{2} - 13 x + 5

= ln (3) + 7 x^{2} - 13 x + 5

lo g_{b} (u^{5} v^{2})

- ln (x) + ln (c)

\frac{1}{3} lo g_{c} (x) + 4 lo g_{c} (y) - 3 lo g_{c} (x)

- lo g_{10} (8.1 \times 1 0^{- 5})

ln (\frac{e ^{6}}{9})

What is ln(3e^{7x^2-13x+5}) ?
The solution to ln(3e^{7x^2-13x+5}) is ln(3)+7x^2-13x+5