Question

Solve for x : (49)^{x + 4} = 7² x (343)^{x + 1}

Answer 1

(49)^{x + 4} = 7² x (343)^{x + 1}

⇒ ( 7 x 7 )^{x + 4} = 7² ( 7 x 7 x 7 )^{( x + 1 )}

⇒ ( 7² )^{x + 4}  = 7²( 7³ )^{( x + 1 )}

⇒ 7^{( 2x + 8 )} = 7² x 7^{3x + 3}

⇒ 7^{( 2x + 8 )} = 7^{3x + 3 + 2}

⇒ 7^{( 2x + 8 )} = 7^{3x + 5}
We know that if bases are equal, the powers are equal
⇒ 2x + 8 = 3x + 5
⇒ 3x - 2x = 8 - 5
⇒ x = 3