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Arlecino [84]
2 years ago
10

Determine the value of x to the nearest thousandth in the equation 8(2)^x+3=48

Mathematics
1 answer:
solong [7]2 years ago
8 0

You probably mean either

8\cdot2^x + 3 = 48

or

8\cdot2^{x+3} = 48

Write 8 = 2³, so that in the first interpretation,

8\cdot2^x = 2^3 \cdot 2^x = 2^{x + 3}

and in the second,

8\cdot2^{x+3} = 2^3 \cdot 2^{x+3} = 2^{x + 6}

Then in the first interpretation, we have

2^{x + 3} + 3 = 48 \implies 2^{x + 3} = 45 \implies x + 3 = \log_2(45) \implies x = \log_2(45) - 3 \approx \boxed{2.492}

Otherwise, the second interpretation gives

2^{x + 6} = 48 \implies x + 6 = \log_2(48) \implies x = \log_2(48) - 6 \approx -0.415

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