Question

Log14/3 +log11/5-log22/15=log

Answer 1

Answer:

log 7

Step-by-step explanation:

Adding the first values :

Applied Rule : log a + log b = log(ab)

⇒ log (14/3) + log (11/5)

⇒ log (14/3 × 11/5)

⇒ log (154/15)

Subtracting the second values :

Applied Rule : log a - log b = log(a/b)

⇒ log (154/15 ÷ 22/15)

⇒ log (154 ÷ 22)

⇒ log 7

Answer 2

Answer:

$log7$

Step-by-step explanation:

when adding logs, apply the log rule: $\log _a\left(x\right)+\log _a\left(y\right)=\log _a\left(xy\right)$

∴  $\log\left(\frac{14}{3}\right)+\log\left(\frac{11}{5}\right)=\log\left(\frac{14}{3}\cdot \frac{11}{5}\right)$

when subtracting logs, apply the log rule: $\log _a\left(x\right)\:-\:\log _a\left(y\right)=\log _a\left(\frac{x}{y}\right)$

$\log\left(\frac{14}{3}\cdot \frac{11}{5}\right)-\log\left(\frac{22}{15}\right)=\log\left(\frac{\frac{14}{3}\cdot \frac{11}{5}}{\frac{22}{15}}\right)\\\\=\log\left(7\right)$