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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]