Question

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Answer 1

Răspuns:

vezi rezolvarea în anexa foto

Answer 2

$\displaystyle\bf\\16a)\\\\log_2\bigg(\frac{8}{x}\bigg)\cdot log_x\,2=1\\\\\bigg(log_2\,8-log_2\,x\bigg)\cdot \frac{1}{log_2\,x}=1\\\\log_2\,8\cdot\frac{1}{log_2\,x}-log_2\,x\cdot \frac{1}{log_2\,x}=1\\\\\frac{log_2\,8}{log_2\,x}-\frac{log_2\,x}{log_2\,x}=1\\\\\frac{log_2\,8}{log_2\,x}-1=1\\\\\frac{log_2\,8}{log_2\,x}=2\\\\log_2\,8=2\cdot log_2\,x\\\\log_2\,8=log_2\,x^2\\\\x^2=8\\\\x=\sqrt{8}\\\\x>0\\\\\boxed{\bf x=2\sqrt{2}}$