Question

(5)^x+1 + (5)^x =130
how to find the value of x ? ​

Answer 1

Step-by-step explanation;

${5}^{x + 1} + {5}^{x - 1} = 130 \\ ({5}^{x} \times 5 )+ ({5}^{x} \times {5}^{ - 1} )= 130 \\ {5}^{x} (5 + \frac{1}{5} ) = 130 \\ {5}^{x} \times \frac{26}{5} = 130 \\ {5}^{x} = \frac{130 \times 5}{26} \\ {5}^{x} = 5 \times 5 \\ {5}^{x} = {5}^{2} \\ x = 2$