What is the value of n in the equation 2.3 × 10^9 = (1 × 10^3)(2.3 × 10^n)?
A) 5
B) 6
C) 7
D) 8
What is the value of n in the equation 2.3 × 10^9 = (1 × 10^3)(2.3 × 10^n)?
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To solve the equation (2.3 times 10^9 = (1 times 10^3)(2.3 times 10^n)), we can simplify the right side:
1. Distribute (1 times 10^3):
[
(1 times 10^3)(2.3 times 10^n) = 2.3 times 10^{3+n}
]
2. Now, we rewrite the equation:
[
2.3 times 10^9 = 2.3 times 10^{3+n}
]
3. Since the (2.3) terms are the same, we can set the exponents equal to each other:
[
9 = 3 + n
]
4. Solve for (n):
[
n = 9 – 3 = 6
]
Thus, the value of (n) is 6. The correct answer is B) 6.