Question

Логарифмические уравнения.

Answer 1

Ответ:

Объяснение:

$\displaystyle\\(16^{0.25-0.5log_24}+25^{log_{125}8})*49=\\ \\ (16^{0.25-0.5*2}+5^{2*log_52})}*49=\\ \\ (16^{0.25-1}+5^{log_54})*49=\\ \\ ((2^4)^{-\frac{3}{4} }+4)*49=(2^{-3}+4)*49=\frac{33}{8} *49=4.125*49=202.125$

$\displaystyle\\10log_\sqrt{2}}log_\sqrt{2}}\sqrt{\sqrt{\sqrt{2} } } }=\\ \\ \\ 10log_\sqrt{2}}log_\sqrt{2}}(\sqrt{2})^\frac{1}{4} =10log_\sqrt{2}}\frac{1}{4} =10log_\sqrt{2}}(\sqrt{2})^{-4} =10*(-4)=-40$

$\displaystyle\\4^{(log_45)^2}*5^{-\frac{1}{log_54}} =(4^{log_45})^{log_45}*5^{-\frac{1}{log_54}} =\\\\ 5^{log_45}*5^{-\frac{1}{log_54}} =5^{{log_45-\frac{1}{log_54}}}=\\ \\ 5^{(log_45*log_54-1)/log_54)}=5^{(1-1)/log_54)}=5^0=1$