Question

calcule o valor de x para os seguintes logaritimos; A) log2x=7 B) logx81=4 C) logx125/8=3 D) log5/2 x=1.

Answer 1

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A)

$\log_2x=7 \\ \\ x=2^7 \\ x=128$ 

B)

$\log_x81=4 \\ \\ x^4=81 \\ \\ x= \sqrt[4]{81} \\ \\ x= \sqrt[4]{3^4} \\ \\ x=3$ 

C)

$\log_x \frac{125}{8} =3 \\ \\ x^3= \frac{125}{8} \\ \\ x= \sqrt[3]{ \frac{125}{8} } \\ \\ x= \sqrt[3]{ \frac{5^3}{2^3} } \\ \\ x= \frac{5}{2}$  

D)

$\log_{ \frac{5}{2} }x=1 \\ \\ x= \frac{5}{2}$