Simplify
8(2^x-1)=64
Since 8^2=64, set 2^x-1=2, 2^1=2 so x-1=1, x=?
I'm assuming x-1 is the exponent.
8 * 2^(x-1) = 64,
2^3 * 2^(x-1) = 2^6,
Add the exponents on the left side:
3 + x - 1 = x + 2,
2^(x+2) = 2^6,
The exponent on both sides has the
same base(2). Therefore,
x + 2 = 6,
x = 4.
Check: substitute 4 for x in the given Eq:
8 * 2^(4-1) =
8 * 2^3 = 8 * 8 = 64.
To simplify the given equation, 8(2^x - 1) = 64, we can follow these steps:
1. Distribute the 8 to both terms inside the parentheses:
8 * 2^x - 8 = 64
2. Simplify further:
2^(x+3) - 8 = 64
3. Add 8 to both sides of the equation to isolate the exponential term:
2^(x+3) = 72
Now, we need to solve for x to fully simplify the equation. Since 2^(x+3) = 72, we can rewrite it as an exponential equation in terms of a common base, such as 2:
2^(x+3) = 2^3 * 3^2
Using the property of exponents, we know that if two exponents are equal, then their bases must also be equal. So, we can set the exponents equal to each other:
x + 3 = 3 + 2
Now, solve for x:
x = 2
Therefore, the simplified solution for the equation 8(2^x - 1) = 64 is x = 2.