1. The first expression is $2\log_{10}(x) = \log_{10}(50)$. This is an equation involving logarithms, so it is a **logarithmic equation**. 2. The second expression is $\log_3(x + 1) \geq 1$. This is an inequality involving logarithms, so it is a **logarithmic inequality**. 3. The third expression is $\ln(x - 1) = 0$. This is an equation involving the natural logarithm, so it is a **logarithmic equation**. Summary: - $2\log_{10}(x) = \log_{10}(50)$ is a logarithmic equation. - $\log_3(x + 1) \geq 1$ is a logarithmic inequality. - $\ln(x - 1) = 0$ is a logarithmic equation.