Solve for x 2.3^x=81-3^x thanks
Assuming you mean
3^x = 81 - 3^x
2*3^x = 3^4
log32 + x = 4
x = 4 - log32
Somehow I suspect a typo.
To solve this equation, we will first simplify it by rewriting 81 as 3^4.
2.3^x = 3^4 - 3^x
Next, we subtract 3^x from both sides to isolate terms with x on one side of the equation.
2.3^x - 3^x = 3^4 - 3^x
To combine the terms on the left side, we can factor out a common factor of (3^x).
(2.3^x - 3^x) = (3^4 - 3^x)
Now, we can factor out (3^x) from the left side.
(1 - 1.3^x) * (3^x) = 3^4 - 3^x
Now, we can divide both sides of the equation by (1 - 1.3^x) to solve for (3^x).
(3^x) = (3^4 - 3^x) / (1 - 1.3^x)
To solve for (3^x), we will substitute the value (3^x) = y.
y = (3^4 - y) / (1 - 1.3^x)
Next, we can multiply both sides of the equation by (1 - 1.3^x).
y * (1 - 1.3^x) = 3^4 - y
Expanding the left side gives us:
y - 1.3^x * y = 3^4 - y
Now, we can add 1.3^x * y to both sides of the equation.
y + 1.3^x * y = 3^4
Factoring out y on the left side gives us:
y * (1 + 1.3^x) = 3^4
Finally, we can divide both sides of the equation by (1 + 1.3^x) to solve for y.
y = 3^4 / (1 + 1.3^x)
Now that we have the value of y, we can substitute it back into the equation (3^x = y) to solve for x:
3^x = 3^4 / (1 + 1.3^x)
Since the bases are the same, we can equate the exponents:
x = 4 / (1 + 1.3^x)
At this point, it may not be possible to solve for x algebraically. You can use numerical methods, such as iteration or a graphing calculator, to approximate the value of x.