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 for ( n ) in the equation ( 2.3 times 10^9 = (1 times 10^3)(2.3 times 10^n) ), we can simplify the right side.
1. Start by distributing ( 1 times 10^3 ):
[
(1 times 10^3)(2.3 times 10^n) = 2.3 times 10^{3+n}
]
2. Now the equation looks like this:
[
2.3 times 10^9 = 2.3 times 10^{3+n}
]
3. Since the coefficients (2.3) on both sides are equal, 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 ).