To solve this equation for x, we can first simplify the terms on the left side of the equation:
229^(x-1) - 1/33^(x+3) + 1/3*3^(x+2) = 4
We know that 9 = 3^2, so we can rewrite the first term as:
223^(2(x-1)) = 223^(2x-2) = 22*9^x
Now, let's simplify the second and third terms:
So our equation simplifies to:
22*9^x = 4
Dividing both sides by 22:
9^x = 4/229^x = 2/11
Now we need to solve for x. Since 9 = 3^2, we can rewrite the equation as:
(3^2)^x = 2/113^2x = 2/11
3^2x = 2/11
Taking the natural logarithm of both sides:
2x * ln(3) = ln(2/11)
2x = ln(2/11) / ln(3)x = (ln(2/11) / ln(3)) / 2
Therefore, x ≈ -1.227981.
To solve this equation for x, we can first simplify the terms on the left side of the equation:
229^(x-1) - 1/33^(x+3) + 1/3*3^(x+2) = 4
We know that 9 = 3^2, so we can rewrite the first term as:
223^(2(x-1)) = 223^(2x-2) = 22*9^x
Now, let's simplify the second and third terms:
1/33^(x+3) + 1/33^(x+2)= - 1/3 3 3^(x+2) + 1/3 3^2 3^x
= -3^(x+2) + 3^(x+2)
= 0
So our equation simplifies to:
22*9^x = 4
Dividing both sides by 22:
9^x = 4/22
9^x = 2/11
Now we need to solve for x. Since 9 = 3^2, we can rewrite the equation as:
(3^2)^x = 2/11
3^2x = 2/11
3^2x = 2/11
Taking the natural logarithm of both sides:
2x * ln(3) = ln(2/11)
2x = ln(2/11) / ln(3)
x = (ln(2/11) / ln(3)) / 2
Therefore, x ≈ -1.227981.