Question

log 7 - log 2 + log 16 - 2log 3 - log7/45 = 1 + log n . find n

Answer 1

$log 7 - log 2 + log 16 - 2log 3 - log \frac{7}{45} = 1 + log n \\ \\ log 7 - log 2 + log 16 - log {3}^{2} - log \frac{7}{45} - 1 = log n$

$log 7 - log 2 + log 16 - log {3}^{2} - log \frac{7}{45} - log10 = log n \\ \\ log 7 + log 16 - log 9 - log \frac{7}{45} - log10 = log n$

$log( \frac{7 \times 16 \times 45}{9 \times 10 \times 7}) = log \: n$

$n = \frac{7 \times 16 \times 45}{9 \times 10 \times 7} = 8$