Question

3) Calcule:
a) log 2/3 (8/27) = x
b) logx 0,0016 = 4​

Answer 1

Resposta:

$\textsf{Leia abaixo}$

Explicação passo a passo:

$\mathsf{log_{\frac{2}{3}}\:\dfrac{8}{27} = x}$

$\mathsf{\left(\dfrac{2}{3}\right)^x = \left(\dfrac{8}{27}\right)}$

$\mathsf{\left(\dfrac{2}{3}\right)^x = \left(\dfrac{2^3}{3^3}\right)}$

$\mathsf{\left(\dfrac{2}{3}\right)^x = \left(\dfrac{2}{3}\right)^3}$

$\boxed{\boxed{\mathsf{x = 3}}}$

$\mathsf{log_x\:0,0016 = 4}$

$\mathsf{x^4 = 0,0016}$

$\mathsf{x^4 = \dfrac{16}{10.000}}$

$\mathsf{x^4 = \dfrac{2^4}{10^4}}$

$\mathsf{x^4 = \left(\dfrac{2}{10}\right)^4}$

$\boxed{\boxed{\mathsf{x = \dfrac{1}{5}}}}$