Question

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

Answer 1

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`