What is 5ln((4x-1)/(2x+1))+sqrt(x^2+3)-2e^0 ?

The solution to 5ln((4x-1)/(2x+1))+sqrt(x^2+3)-2e^0 is 5(ln(4x-1)-ln(2x+1))+sqrt(x^2+3)-2

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simplify 5ln((4x-1)/(2x+1))+sqrt(x^2+3)-2e^0

simplify

5 ln (\frac{4 x - 1}{2 x + 1}) + x^{2} + 3 - 2 e^{0}

5 (ln (4 x - 1) - ln (2 x + 1)) + x^{2} + 3 - 2

Solution steps

5 ln (\frac{4 x - 1}{2 x + 1}) + x^{2} + 3 - 2 e^{0}

Apply log rule:

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

ln (\frac{4 x - 1}{2 x + 1}) = ln (4 x - 1) - ln (2 x + 1)

= 5 (ln (4 x - 1) - ln (2 x + 1)) + x^{2} + 3 - 2 e^{0}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 5 (ln (4 x - 1) - ln (2 x + 1)) + x^{2} + 3 - 2 \cdot 1

Multiply the numbers:

2 \cdot 1 = 2

= 5 (ln (4 x - 1) - ln (2 x + 1)) + x^{2} + 3 - 2

2 [ln (x) - ln (x + 1) - ln (x - 1)]

ln (6 (ln (x))^{8})

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

ln (\frac{729}{625})

lo g_{10} (x^{2} - 5 x + 6) - lo g_{10} (x - 3)

What is 5ln((4x-1)/(2x+1))+sqrt(x^2+3)-2e^0 ?
The solution to 5ln((4x-1)/(2x+1))+sqrt(x^2+3)-2e^0 is 5(ln(4x-1)-ln(2x+1))+sqrt(x^2+3)-2