Which of the following statements is not correct?

1log₁₀ 10 = 1
2log (2 + 3) = log (2 x 3)
3log₁₀ 1 = 0
4log (1 + 2 + 3) = log 1 + log 2 + log 3

Answer:- 1

Explanation:-

Solution:

\begin{aligned} A  =  Since lo g_{a} a = 1, so lo g_{10} 10 = 1 \\ B = log (2 + 3) = 5 \\ and log (2 \times 3) = log 6 \\ = log 2 + log 3 \\ ∴ log (2 + 3) \neq log (2 \times 3) . \\ C = Since lo g_{a} 1 = 0, s o lo g_{10} 1 = 0. \\ D  =  log (1 + 2 + 3) = log 6 \\ = log (1 \times 2 \times 3) \\ = log 1 + log 2 + log 3. \\ So (2) is incorrect \end{aligned}

$\eqalign{ & {\text{A = Since lo}}{{\text{g}}_a}a = 1,{\text{ so lo}}{{\text{g}}_{10}}10 = 1 \cr & \cr & B = \,{\text{log}}\left( {2 + 3} \right) = 5\, \cr & \,\,\,{\text{and log}}\left( {2 \times 3} \right) = {\text{log}}6 \cr & = {\text{log}}2 + {\text{log}}3 \cr & \therefore \,{\text{log}}\left( {2 + 3} \right) \ne {\text{log}}\left( {2 \times 3} \right). \cr & \cr & C = \,{\text{ Since lo}}{{\text{g}}_a}1 = 0,so{\text{ lo}}{{\text{g}}_{10}}1 = 0. \cr & \cr & {\text{D = log}}\left( {1 + 2 + 3} \right) = {\text{ log}}6 \cr & = {\text{ log}}\left( {1 \times 2 \times 3} \right) \cr & = {\text{ log}}1 + {\text{ log}}2 + {\text{ log}}3. \cr & {\text{So (2) is incorrect}} \cr}$