Question

Determine o valor de x, sabendo que x= log (base 3) 4 × log (base 2 ) 3

Answer 1

Vamos passar o log[3] 4 para a base 2:

log[3] 4 = log[2] 4 / log[2] 3 

Assim:

x = log[2] 4 / log[2] 3 x log[2] 3 
x = log[2] 4
2^x = 2²
x = 2

O [ ] coloquei para indicar a base

Answer 2

$x = log_{3} 4* log_{2} 3 \\ log_{3} 4= \frac{log_{4} }{log_{3} } \\ log_{2} 3= \frac{log_{3} }{log_{2} } \\ \\ Logo:$


$\frac{log_{4} }{log_{3}} * \frac{log_{3} }{log_{2} } \\ \\ =\frac{log_{4} }{log_{2}} \\ \\ \\ = \\ log_24=x \\ 2^x=4 \\ 2^x=2^2 \\ x=2$