Solving the Equation: 1/2×2^n + 4×2^n = 9×2^5
In this article, we will explore the solution to the equation:
1/2×2^n + 4×2^n = 9×2^5
To solve this equation, we need to simplify and combine like terms.
Step 1: Simplify the Left Side
The left side of the equation is:
1/2×2^n + 4×2^n
We can combine these terms by factoring out 2^n:
(1/2 + 4)×2^n
= (0.5 + 4)×2^n
= 4.5×2^n
Step 2: Simplify the Right Side
The right side of the equation is:
9×2^5
Step 3: Equate the Two Expressions
Now, we equate the simplified left side to the simplified right side:
4.5×2^n = 9×2^5
Step 4: Solve for n
To solve for n, we can divide both sides of the equation by 4.5:
2^n = (9/4.5)×2^5
2^n = 2^5
Since the bases are the same (2), we can equate the exponents:
n = 5
Therefore, the value of n that satisfies the equation is 5.
In conclusion, the solution to the equation 1/2×2^n + 4×2^n = 9×2^5 is n = 5.
