Question

Solve
log (2x - 2) – log (11.66 – x) = 1 + log3
​

Answer 1

Answer:

$log(2x - 2) - log (11.66-x)= 1 + log3 \\ log \frac{(2x - 2)}{(11.66 - x)} = log10 + log3 \\ ..( \because \: log \: 10 = 1) \\ log \frac{(2x - 2)}{(11.66 - x)} = log(10 \times 3) \\ log \frac{(2x - 2)}{(11.66 - x)} = log30 \\ \frac{2x - 2}{11.66 - x} = 30 \\ \frac{2(x - 1)}{11.66 - x} = 30 \\ \frac{x - 1}{11.66 - x} = 15 \\ x - 1 = 15(11.66 - x) \\ x - 1 = 174.9 - 15x \\ x + 15x = 174.9 + 1 \\ 16x = 175.9 \\ x = \frac{175.9}{16} \\ x = 10.99375 \\ x \approx11$