Question

log de 729/64
base 2/3​

Answer 1

log(⅔) 729/64 = n

(2/3)ⁿ = 729/64

(2/3)ⁿ = 3⁶/2⁶

(2/3)ⁿ = (3/2)⁶

(2/3)ⁿ = (2/3)⁻⁶

n = -6 ✓

Answer 2

729=27²

64=8²

$log_{ \frac{2}{3} }( \frac{729}{64} ) = log_{ \frac{2}{3} }( { \frac{27}{8}) }^{2} \\ = log_{ \frac{2}{3} }( { \frac{3}{2} )}^{6} = log_{ \frac{2}{3}}( { \frac{2}{3} )}^{ - 6} = - 6$