7.Use the like-bases property and exponents to solve the equation left(frac{1}{3}right)^{x+9}=3^{2 x+3}

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Accepted Answer

Step:1 ：Rewrite the bases in a similar form. We can rewrite 1/3 as (3^{-1}) and then apply the properties of exponents to simplify the equation.Step:2 ：Equating the exponents of the similar bases, we get the equation (-x - 9 = 2x + 3).Step:3 ：Solving this equation for x, we get the solution (x = -4).Step:4 ：Substituting (x = -4) into the original equation, we find that both sides of the equation are equal.Step:5 ：The solution to the equation is (boxed{-4}).

Answer

Step: 1 ：Rewrite the bases in a similar form. We can rewrite 1/3 as (3^{-1}) and then apply the properties of exponents to simplify the equation.Step: 2 ：Equating the exponents of the similar bases, we get the equation (-x - 9 = 2x + 3).Step: 3 ：Solving this equation for x, we get the solution (x = -4).Step: 4 ：Substituting (x = -4) into the original equation, we find that both sides of the equation are equal.Step: 5 ：The solution to the equation is (boxed{-4}).

7.Use the like-bases property and exponents to solve the equation $\left(\frac{1}{3}\right)^{x+9}=3^{2 x+3}$

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