Question

Если log3 2=x.Найти log6 64

Answer 1

Ответ: 6x/(x+6)

Объяснение:

log6 64 = 1/log64 6;

log64 6 = log 2^6 6= log 2^6 (2*3)=log 2^6 2 + log 2 ^6 3 = 1/6+ 1/6*log2 3;

log2 3 = 1/log3 2 = 1/x;

log64 6 =1/6+1/x

log6 64 =1/(1/6+1/x)=1/((x+6)/6x)=6x/(x+6)

Answer 2

$log_{3}2=x\\\\log_{6}64=\frac{log_{3}64}{log_{3}6}=\frac{log_{3}2^{6}}{log_{3}(2*3)}=\frac{6log_{3}2}{log_{3}2+log_{3}3}=\frac{6x}{x+1}\\\\Otvet:\boxed{\frac{6x}{x+1}}$