What is ln((e^{(x+2)}(5x+1)^3)/(x^5(2x+1)^7)) ?

The solution to ln((e^{(x+2)}(5x+1)^3)/(x^5(2x+1)^7)) is x+2+3ln(5x+1)-5ln(x)-7ln(2x+1)

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simplify ln((e^{(x+2)}(5x+1)^3)/(x^5(2x+1)^7))

simplify

ln (\frac{e ^{(x + 2)} ( 5 x + 1 ) ^{3}}{x ^{5} ( 2 x + 1 ) ^{7}})

x + 2 + 3 ln (5 x + 1) - 5 ln (x) - 7 ln (2 x + 1)

Solution steps

ln (\frac{e ^{(x + 2)} ( 5 x + 1 ) ^{3}}{x ^{5} ( 2 x + 1 ) ^{7}})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

ln (\frac{e ^{(x + 2)} ( 5 x + 1 ) ^{3}}{x ^{5} ( 2 x + 1 ) ^{7}}) = ln (e^{(x + 2)} (5 x + 1)^{3}) - ln (x^{5} (2 x + 1)^{7})

= ln (e^{x + 2} (5 x + 1)^{3}) - ln (x^{5} (2 x + 1)^{7})

Apply log rule:

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

ln (e^{x + 2} (5 x + 1)^{3}) = ln (e^{x + 2}) + ln ((5 x + 1)^{3}), ln (x^{5} (2 x + 1)^{7}) = ln (x^{5}) + ln ((2 x + 1)^{7})

= ln (e^{x + 2}) + ln ((5 x + 1)^{3}) - (ln (x^{5}) + ln ((2 x + 1)^{7}))

Apply log rule:

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

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

= (x + 2) ln (e) + ln ((5 x + 1)^{3}) - (ln (x^{5}) + ln ((2 x + 1)^{7}))

Apply log rule:

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

ln ((5 x + 1)^{3}) = 3 ln (5 x + 1)

= (x + 2) ln (e) + 3 ln (5 x + 1) - (ln (x^{5}) + ln ((2 x + 1)^{7}))

Apply log rule:

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

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

= (x + 2) ln (e) + 3 ln (5 x + 1) - (5 ln (x) + ln ((2 x + 1)^{7}))

Apply log rule:

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

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

= (x + 2) ln (e) + 3 ln (5 x + 1) - (5 ln (x) + 7 ln (2 x + 1))

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

= x + 2 + 3 ln (5 x + 1) - (5 ln (x) + 7 ln (2 x + 1))

- (5 ln (x) + 7 ln (2 x + 1)) : - 5 ln (x) - 7 ln (2 x + 1)

= x + 2 + 3 ln (5 x + 1) - 5 ln (x) - 7 ln (2 x + 1)

\frac{19.16}{0.004 \cdot 0.02} ln (\frac{1}{1 - 0.9})

ln (\frac{e ^{3} y ^{2}}{x})

0.4 lo g_{2} (0.4) + 0.6 lo g_{2} (0.6)

4 \cdot ln (\frac{1}{2})

\frac{1}{2} ln (tan (\frac{x}{2}))

What is ln((e^{(x+2)}(5x+1)^3)/(x^5(2x+1)^7)) ?
The solution to ln((e^{(x+2)}(5x+1)^3)/(x^5(2x+1)^7)) is x+2+3ln(5x+1)-5ln(x)-7ln(2x+1)