Answer:
the solution to the equation 2x^+4=8^x is x = 1.
Explanation:
To solve the equation 2x^+4=8^x, we can start by simplifying both sides of the equation.
First, we can rewrite 8^x as (2^3)^x, using the property that 8 is equal to 2 raised to the power of 3.
So, the equation becomes:
2x^+4 = (2^3)^x
2x^+4 = 2^(3x)
Next, we can rewrite 2x^+4 as 2^2 * 2^x, using the property that a^b * a^c = a^(b+c).
So, the equation becomes:
2^2 * 2^x = 2^(3x)
2^(x+2) = 2^(3x)
Now, we can equate the exponents on both sides of the equation:
x + 2 = 3x
2x = 2
x = 1
Therefore, the solution to the equation 2x^+4=8^x is x = 1.