Answer:
x=7
Explanation:
(x=7) To solve the equation 2^x = 128, we can express both sides of the equation as powers of the same base, in this case, 2. By rewriting 128 as a power of 2, we can equate the exponents.
To express 128 as a power of 2, we need to find the exponent that, when raised to 2, equals 128. We can do this by continuously dividing 128 by 2 until we reach 1.
128 ÷ 2 = 64
64 ÷ 2 = 32
32 ÷ 2 = 16
16 ÷ 2 = 8
8 ÷ 2 = 4
4 ÷ 2 = 2
2 ÷ 2 = 1
From the steps above, we can see that 128 can be expressed as 2^7. Now, we can set up the equation:
2^x = 2^7
Since both sides have the same base, we can equate the exponents:
x = 7
Therefore, the value of x that satisfies the equation 2^x = 128 is x = 7.
In simpler terms, we found that 128 can be expressed as 2^7. This means that x must be equal to 7 for the equation 2^x = 128 to hold true.
I hope this explanation helps! Let me know if you have any further questions.