Final answer:
To solve the equation, ((1/3)^(3x+7))=(1/9)^4, we simplify both sides and apply the exponent rule. After equating the exponents, we solve for x by isolating it. The solution is x = 1/3.
Step-by-step explanation:
To solve the equation ((1/3)^{3x+7})=(1/9)^4, we need to first simplify both sides of the equation. We can simplify the left side by applying the exponent rule that states (a^b)^c = a^(b*c). Applying this rule, we can write the equation as (1/3)^(3x+7) = (1/3)^(4*2).
Now that the bases are the same, we can equate the exponents. So, 3x + 7 = 4*2. Simplifying further, 3x + 7 = 8.
To solve for x, we subtract 7 from both sides of the equation, giving us 3x = 1. Finally, we divide both sides by 3 to isolate x, resulting in x = 1/3.
Learn more about Solving exponential equations