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2^x=128 Solve the exponential equation by expressing each side as a power of the same base and then equating exponents

User Younggotti
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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.

User Martin Milan
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