Question

log
$log_{9} \sqrt{3 \sqrt{3 \sqrt{3} } }$

Answer 1

Answer:

7 / 16

Step-by-step explanation:

$\log_9 \sqrt{3\sqrt{3\sqrt3}} \\= \frac12 \log_9 3\sqrt{3\sqrt3}\\= \frac12 \left( \log_9 3 + \log_9 \sqrt{3\sqrt3}\right) \\= \frac12 \left( \frac12 + \frac12\log_9 3\sqrt 3 \right) \\= \frac14 + \frac14\log_9 3\sqrt3 \\= \frac14 + \frac14 \left( \log_9 3 + \log_9 \sqrt 3 \right) \\= \frac14 + \frac14 \left( \frac12 + \frac12 \log_9 3 \right) \\= \frac14 + \frac18 + \frac 18\log_9 3 \\= \frac14 + \frac18 + \frac18\frac12 \\= \frac14 + \frac18 + \frac1{16} \\= \frac{7}{16}$