Answer: 12.25 or Approximately 12.3
Step-by-step explanation:
To solve this problem, we first need to solve for x. We are given with 2ˣ=7.
To get x alone, we want to use natural log, or ln.
[tex]xln(2)=ln(7)[/tex] [once you find ln of both sides, you bring the x to the front]
[tex]x=\frac{ln(7)}{ln(2)}[/tex] [divide both sides by ln(2)]
[tex]x=2.81[/tex]
We now know that x is approximately 2.81. We can plug that in to find 4ˣ⁻¹.
[tex]4^(^x^-^1^)[/tex] [plug in x]
[tex]4^(^2^.^8^1^-^1^)[/tex] [parenthesis]
[tex]4^{1.81}[/tex] [exponent]
[tex]12.3[/tex]
The answer is approximately 12.3. To get a more exact answer, you would plug in [tex]\frac{ln(7)}{ln(2)}[/tex] into x.
[tex]4^{\frac{ln(7)}{ln(2)}-1 }[/tex]
[tex]12.25[/tex]
The exact answer would be 12.25. This is close to 12.3 since it is rounded up to one decimal place.
