Answer:
x = 2
Step-by-step explanation:
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
Note that 49 = 7² and 343 = 7³
Consider the left side, that is
[tex]\frac{7^{2x+1} }{7^2}[/tex] = [tex]7^{(2x+1-2)}[/tex] = [tex]7^{(2x-1)}[/tex] , thus
[tex]7^{(2x-1)}[/tex] = 7³
Since bases on both sides are equal, equate the exponents, that is
2x - 1 = 3 ( add 1 to both sides )
2x = 4 ( divide both sides by 2 )
x = 2
