1 Answer

Iammrmehul · Answer 1 · 2023-06-12T07:55:57+0000

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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