Question

If in a $\Delta ABC,\tan A+\tan B+\tan C>0$, then the triangle is

Answer 1

Use $lo{g}_{a}b=\frac{lo{g}_{c}b}{lo{g}_{c}a}$.....$\left(1\right)$

Here consider c=10(standard log)

$xyz=lo{g}_{5}7\times lo{g}_{7}27\times lo{g}_{3}5$

Using $\left(1\right)$, we get

$xyz=\frac{lo{g}_{10}7}{lo{g}_{10}5}\times \frac{lo{g}_{10}27}{lo{g}_{10}7}\times \frac{lo{g}_{10}5}{lo{g}_{10}3}=\frac{lo{g}_{10}27}{lo{g}_{10}3}=\frac{lo{g}_{10}{3}^3}{lo{g}_{10}3}=3$

Hence proved.