Question

Помогите решить уравнения пожалуйста

Answer 1

Ответ:

a)

${3}^{x} = 81 \\ {3}^{x} = {3}^{4} \\ x = 4$

б)

${( \frac{1}{2}) }^{x} = 64 \\ {2}^{ - x} = {2}^{6} \\ x = - 6$

в)

$log_{2}(x) = - 3 \\ x = {2}^{ - 3} \\ x = \frac{1}{8}$

г)

$log_{2}(3 - x) = 0 \\ 3 - x = 1 \\ - x = - 2 \\ x = 2$

д)

${2}^{5 + x} = {2}^{5x - 4} \\ 5 + x = 5x - 4 \\ - 4x = - 9 \\ x = \frac{9}{4}$

е)

$lg(x) = t \\ {t}^{2} + 2t - 3 = 0 \\ d = 4 + 12 = 16 \\ t1 = \frac{ - 2 + 4}{2} = 1 \\ t2 = - 3 \\ \\ lg(x) = 1 \\ x1 = 10 \\ \\ lg(x) = - 3 \\ x2 = {10}^{ - 3} = 0.001$