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

Sagot :

LammettHash

You probably mean either

[tex]8\cdot2^x + 3 = 48[/tex]

or

[tex]8\cdot2^{x+3} = 48[/tex]

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

[tex]8\cdot2^x = 2^3 \cdot 2^x = 2^{x + 3}[/tex]

and in the second,

[tex]8\cdot2^{x+3} = 2^3 \cdot 2^{x+3} = 2^{x + 6}[/tex]

Then in the first interpretation, we have

[tex]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}[/tex]

Otherwise, the second interpretation gives

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

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