Question

Find the value of log 16/81 to the base 2/3* log 1/64 to the base 4.​

Answer 1

$log_{ \frac{2}{3} }( \frac{16}{81} )$

$log_{ \frac{2}{3} }( \frac{ {2}^{4} }{ {3}^{4} } )$

$\frac{4}{4} log_{\frac{2}{3} }( \frac{2}{3} )$

$1 \times 1$

1

$log_{4}(\frac{1}{64} )$

$log_{4}( \frac{1}{ {4}^{2} } )$

$- 2 log_{4}(4)$

$- 2 \times 1 = - 2$