What is ln(5e^{(2x+1)}(2x^5+2)^7) ?

The solution to ln(5e^{(2x+1)}(2x^5+2)^7) is ln(5)+2x+1+7ln(2x^5+2)

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simplify ln(5e^{(2x+1)}(2x^5+2)^7)

simplify

ln (5 e^{(2 x + 1)} (2 x^{5} + 2)^{7})

ln (5) + 2 x + 1 + 7 ln (2 x^{5} + 2)

Solution steps

ln (5 e^{(2 x + 1)} (2 x^{5} + 2)^{7})

Apply log rule:

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

ln (5 e^{(2 x + 1)} (2 x^{5} + 2)^{7}) = ln (5) + ln (e^{(2 x + 1)}) + ln ((2 x^{5} + 2)^{7})

= ln (5) + ln (e^{(2 x + 1)}) + ln ((2 x^{5} + 2)^{7})

Apply log rule:

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

ln (e^{(2 x + 1)}) = (2 x + 1) ln (e)

= ln (5) + (2 x + 1) ln (e) + ln ((2 x^{5} + 2)^{7})

Apply log rule:

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

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

= ln (5) + (2 x + 1) ln (e) + 7 ln (2 x^{5} + 2)

(2 x + 1) ln (e) = 2 x + 1

= ln (5) + 2 x + 1 + 7 ln (2 x^{5} + 2)

ln (3 x^{2} - 9) + ln (\frac{1}{3 x})

ln (\frac{0.1}{0.3})

ln (\frac{0.5}{1620})

ln (∣ x - 1 ∣^{5}) - ln (∣ x ∣^{3}) + c

10 ln ∣ P ∣ - 10 ln ∣ P - 1000000 ∣

What is ln(5e^{(2x+1)}(2x^5+2)^7) ?
The solution to ln(5e^{(2x+1)}(2x^5+2)^7) is ln(5)+2x+1+7ln(2x^5+2)