Question

Помогите, спасайте...

Answer 1

$1)\; \; log_{\sqrt7}\; 49\sqrt7=log_{7^{1/2}}\; 7^{5/2}=2\cdot \frac{5}{2}=5\\\\2)\; \; log_{3}\sqrt3\cdot log_3\sqrt[4]3-log_{\sqrt3}3\cdot log_{\sqrt[4]3}3=\\\\=log_33^{1/2}\cdot log_33^{1/4}-log_{3^{1/2}}3\cdot log_{3^{1/4}}3=\\\\=\frac{1}{2}\cdot \frac{1}{4}-2\cdot 4=\frac{1}{8}-8=-\frac{63}{8}$

$3)\; \; \sqrt{17}^{log_{17}64}+10^{log_{\sqrt{10}}12}=17^{log_{17}64^{1/2}}+10^{log_{10^{1/2}}12}=\\\\=\sqrt{64}+12^2=8+144=152$