What is the answer to ln((x+5)/x)=3 ?

The answer to ln((x+5)/x)=3 is x= 5/(e^3-1)

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ln((x+5)/x)=3

ln (\frac{x + 5}{x}) = 3

x = \frac{5}{e ^{3} - 1}

Decimal Notation

x = 0.26197 \dots

Solution steps

ln (\frac{x + 5}{x}) = 3

Apply log rules

\frac{x + 5}{x} = e^{3}

Multiply both sides by

x

\frac{x + 5}{x} x = e^{3} x

Simplify

x + 5 = e^{3} x

Solve

x + 5 = e^{3} x : x = \frac{5}{e ^{3} - 1}

x = \frac{5}{e ^{3} - 1}

Verify Solutions:

x = \frac{5}{e ^{3} - 1}

True

The solution is

x = \frac{5}{e ^{3} - 1}

ln (x - 6) = ln (x + 6) - ln (x - 4)

0.63 = ln (x)

lo g_{5} (x) - 1 = 6 lo g_{x} (5)

ln ((x + 2)^{2}) = 6

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

What is the answer to ln((x+5)/x)=3 ?
The answer to ln((x+5)/x)=3 is x= 5/(e^3-1)
Solve for x: ln((x+5)/x)=3
The solution is x= 5/(e^3-1)