WAEC 2022 · Paper 1 · Q3

If $\log_{10}(3x - 1) + \log_{10} 4 = \log_{10}(9x + 2)$ , find the value of $x$ .

Worked solution (try it first)

Adding logs of the same base multiplies the numbers: the left side is $\log_{10} 4(3x - 1)$ .
Equal logs mean equal numbers, so $4(3x - 1) = 9x + 2$ , that is $12x - 4 = 9x + 2$ .
Take $9x$ from both sides and add 4: $3x = 6$ , so $x = 2$ , option C.