$\log 3 - \log 2$
Step 1: The total concentration of $H^+$ ions is calculated as: \[ {HCl contribution} = 0.1 M \times \frac{2}{6} = \frac{0.2}{6} \] \[ {H}_2{SO}_4 { contribution} = 2 \times (0.1 M \times \frac{2}{6}) = \frac{0.4}{6} \] Step 2: Total $H^+$ concentration: \[ [{H}^+] = \frac{0.2}{6} + \frac{0.4}{6} = \frac{0.6}{6} = 0.1 M \] Step 3: pH calculation: \[ {pH} = -\log [H^+] \] \[ {pH} = -\log(0.1) = 1.0 \] Step 4: Therefore, the correct answer is (B).
Let \( I = \int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{\tan^2 x}{1+5^x} \, dx \). Then: