Question

rezolvati ecuatia exponentiala

i) $7^{x} + 7^{x+1} + 2 * 7^{x+2} = 5^{x} - 5^{x+1} + 2 * 5^{x+2}$

Answer 1

$7^x(1+7+98)=5^x(1-5+50) \\ 106*7^x=46*5^x \\ (\frac{7}{5})^x= \frac{46}{106 } \\ ( \frac{7}{5})^x= \frac{23}{53} \\ x= log_{ \frac{7}{5} } \frac{23}{53}$