Question

log a to the base b = c
then ,
log a to the base 1/b = ???
please answer me fastttt friends ....
first answer will be BRAINLIEST

Answer 1

$log_{b}(a) = c \: - - - - - 1 \\ then \\ log_{ \frac{1}{b} }(a) = log_{ {b}^{ - 1} }(a) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{1}{ - 1} log_{b}(a) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 1 log_{b}(a) (from \: 1) \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 1(c) = - c$
Hope this hele u....