Question

log 243 to the base 9

Answer 1

$log_{9}(243) \\ = log_{9}(3 \times 3 \times 3 \times 3 \times 3) \\ = log_{ {3}^{2} }( {3}^{5} ) \\ = (1 \div 2) log_{3}( {3}^{5} ) \\ = (1 \div 2)(5) \\ = 5 \div 2$
here is answer=5/2

Answer 2

log 243 to the base 9

We know that,

243 = 3⁵

so, we have,

$log_9243 = log_93^5$

using the log properties, we have,

$loga^n = n log a$

therefore, we have,

$log_93^5 = 5 log_93$

$5log_93 = 5\log_{3^2}3$

using the log properties, we have,

$5\log_{3^2}3 = 5 \times \dfrac{1}{2} log_33$

$5 \times \dfrac{1}{2} log_33=\dfrac{5}{2}\log_33$

using the log properties, we have,

$log_aa=1$

$\dfrac{5}{2}\log_33 = \dfrac{5}{2} (1)$

$\therefore, log_9 (243) = \dfrac{5}{2}$

log 243 to the base 9 = 5/2