1[tex]\frac{1}{3} x^{x+1}= \frac{1}{81}[/tex]
Answer (1)
Answer:Here's how to solve the equation: 1. Simplify the fractions: - 1 1/3 can be rewritten as 4/3.- 1/81 can be rewritten as 1/3^4. This gives us: (4/3) * x^(x+1) = 1/3^4 2. Express both sides with the same base: - Notice that 4 can be expressed as 2^2.- Now we have: (2^2 / 3) * x^(x+1) = 1/3^4 3. Simplify further: - Move the 3 in the denominator of the left side to the numerator of the right side:2^2 * x^(x+1) = 1 / (3^3 * 3)2^2 * x^(x+1) = 1/3^4 4. Now we have the same base on both sides: - 2^2 * x^(x+1) = 3^(-4) 5. To have the same exponents on both sides, the exponents must be equal: - Since we have 2^2 on the left side, we can rewrite 3^(-4) as (3^(-2))^2 6. Set the exponents equal to each other: - x + 1 = -2 7. Solve for x: - x = -2 - 1- x = -3 Therefore, the solution to the equation is x = -3
