What is the answer to 2*ln(x+3)+4=x ?

The answer to 2*ln(x+3)+4=x is x=-2\W_{-1}(-1/(2e^{7/2)})-3,x=-2\W_{0}(-1/(2e^{7/2)})-3

Solve for x: 2*ln(x+3)+4=x

The solution is x=-2\W_{-1}(-1/(2e^{7/2)})-3,x=-2\W_{0}(-1/(2e^{7/2)})-3

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2 \cdot ln (x + 3) + 4 = x

x = - 2 W_{- 1} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3, x = - 2 W_{0} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3

Decimal Notation

x = 8.96376 \dots, x = - 2.96933 \dots

Solution steps

2 ln (x + 3) + 4 = x

Move

4

to the right side

2 ln (x + 3) = x - 4

Divide both sides by

2

ln (x + 3) = \frac{x - 4}{2}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

e^{l n (x + 3)} = e^{\frac{x - 4}{2}}

Simplify

e^{l n (x + 3)} : x + 3

x + 3 = e^{\frac{x - 4}{2}}

Solve

x + 3 = e^{\frac{x - 4}{2}} : x = - 2 W_{- 1} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3, x = - 2 W_{0} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3

x = - 2 W_{- 1} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3, x = - 2 W_{0} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3

Verify Solutions:

x = - 2 W_{- 1} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3

True

, x = - 2 W_{0} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3

True

The solutions are

x = - 2 W_{- 1} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3, x = - 2 W_{0} (- \frac{1}{2 e ^{\frac{7}{2}}}) - 3

lo g_{7} (2 x + 1) + lo g_{7} (x - 2) = 1

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

lo g_{3} (6 x + 5) = 2

lo g_{10} (4 x) + lo g_{10} (13) = 0

y, x = - lo g_{e} (y)

What is the answer to 2*ln(x+3)+4=x ?
The answer to 2*ln(x+3)+4=x is x=-2\W_{-1}(-1/(2e^{7/2)})-3,x=-2\W_{0}(-1/(2e^{7/2)})-3
Solve for x: 2*ln(x+3)+4=x
The solution is x=-2\W_{-1}(-1/(2e^{7/2)})-3,x=-2\W_{0}(-1/(2e^{7/2)})-3