Final answer:
To find the value of d in the equation (2^d-6) / 2 = 2^9, you can start by multiplying both sides of the equation by 2. This will eliminate the fraction. Then, you can use the rule of exponents to simplify the equation and set the exponents equal to each other. Adding 6 to both sides will give you the value of d, which is 16.
Step-by-step explanation:
To find the value of d in the equation (2^d-6) / 2 = 2^9, we can start by multiplying both sides of the equation by 2. This will eliminate the fraction:
2 * [(2^d-6) / 2] = 2 * 2^9
Canceling out the 2s on the left side gives us:
2^d-6 = 2 * 2^9
Now we can rewrite the equation as:
2^d - 6 = 2^1 * 2^9
Using the rule of exponents that states a^x * a^y = a^(x+y), we can simplify the right side of the equation to:
2^d - 6 = 2^(1+9)
Simplifying further gives us:
2^d - 6 = 2^10
Now we can set the exponents equal to each other:
d - 6 = 10
Adding 6 to both sides gives us:
d = 16