ln(4x+5)=0

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1. Start with the original equation:
\ln(4x+5) = 0

2. Use the property of logarithms that \ln(y) = 0 \implies y = 1:
4x + 5 = 1

3. Subtract 5 from both sides to isolate terms with x:
4x = 1 - 5

4. Simplify the right side:
4x = -4

5. Divide both sides by 4 to solve for x:
x = \frac{-4}{4} = -1

The solution is:
x = -1