What is the answer to ln(x)-1=ln(5+x)-4 ?

The answer to ln(x)-1=ln(5+x)-4 is x=(5e)/(e^4-e)

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ln(x)-1=ln(5+x)-4

ln (x) - 1 = ln (5 + x) - 4

x = \frac{5 e}{e ^{4} - e}

Decimal Notation

x = 0.26197 \dots

Solution steps

ln (x) - 1 = ln (5 + x) - 4

Apply log rules

x e^{4} = (5 + x) e

Solve

x e^{4} = (5 + x) e : x = \frac{5 e}{e ^{4} - e}

x = \frac{5 e}{e ^{4} - e}

Verify Solutions:

x = \frac{5 e}{e ^{4} - e}

True

The solution is

x = \frac{5 e}{e ^{4} - e}

a, lo g_{a} (b) = c

lo g_{4} (3 x + 1) = 2

lo g_{x} (4) = \frac{1}{3}

lo g_{2} (x + 4) = 3 - lo g_{2} (x + 6)

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

What is the answer to ln(x)-1=ln(5+x)-4 ?
The answer to ln(x)-1=ln(5+x)-4 is x=(5e)/(e^4-e)
Solve for x: ln(x)-1=ln(5+x)-4
The solution is x=(5e)/(e^4-e)