If $(5)^{x^2+2x+7} = (125)^{2x+1}$ then the value of x is- 6. If $3^{x+8} = 27^{2x+1}$, then the value of x is –

Explanation

$3^{x+8} = 27^{2x+1}$ $3^{x+8} = (3^3)^{2x+1}$ $3^{x+8} = 3^{6x+3}$ Since the bases of both sides are the same, therefore the powers will also be equal. $\therefore x + 8 = 6x + 3$ $6x - x = 8 - 3$ $5x = 5$ $x = 1$