Question

calcule o valor dos seguintes logaritmos

Answer 1

A)

16^x = 64

4^2x = 4^3  -> Corta as bases

2x = 3

x = 3/2

B)

5^x = 0,000064

5^x = 64 * 10^-6

5^x = 64 * (2*5)^-6

5^x = 64/(2^6 * 5^6)

5^x = 64/( 64 * 5^6)

5^x = 1/5^6 = 5^-6 ---> corta as bases

x = -6

Answer 2

$Resolu\c{c}\~ao \to \left\{\begin{array}{ccc}log_{16}\ 64 = x\\\\16^x = 64\\\\(2^4)^x = 2^6\\\\2^{4x} = 2^6\\\\4x=6\\\\\boxed{\boxed{x = \frac{6}{4} = \frac{3}{2} }}\end{array}\right \to \left\{\begin{array}{ccc}log_5\ 0,000064=x\\\\5^x = 0,000064\\\\5^x = 64*10^{-6}\\\\5^x = 64*(2*5)^{-6}\\\\5^x = 64* \frac{1}{2^{6}}* \frac{1}{5^{6}}\\\\5^x = 64* \frac{1}{64}* \frac{1}{5^6}\\\\5^x = 5^{-6}\\\\\boxed{\boxed{x= -6}} \end{array}\right$

Espero ter ajudado. :))