4. Prove: 2^n + 2^n = 2^n+1
correct, if you write it as
2^(n+1)
x 2 - 4 for x = 5
To prove the equation 2^n + 2^n = 2^(n+1), we can use the properties of exponents.
The left side of the equation is 2^n + 2^n. To combine these terms, we need to have the same base, which is 2. By using the law of exponents, we can add the exponents together:
2^n + 2^n = 2^(n+n)
Now, we simplify the right side of the equation, which is 2^(n+1). Using the property of exponents, when you have a power raised to another power, you can multiply the exponents:
2^(n+n) = 2^(2n)
Now we can compare the left side and the right side of the equation:
2^n + 2^n = 2^(n+n) = 2^(2n)
To prove that the equation holds, we need to show that 2^(2n) is equal to 2^(n+1). By comparing the exponents, we can see that 2n = n + 1 when n = 1 (in other words, if the exponent on the left side is n = 1, then the exponent on the right side will also be 1+1=2).
Therefore, when n = 1, the equation 2^n + 2^n = 2^(n+1) is proven to be true.