Answer:
x = -3
Step-by-step explanation:
Step 1: Take log of both sides.
- [tex]log(4^x)=log(2^x^-^3)[/tex]
- [tex]x*(log(4)) = (x-3)*(log(2))[/tex]
- [tex]x = (\frac{log(2)}{log(4)}) * (x-3)[/tex]
- [tex]x = 0.5 * (x-3)[/tex]
Step 2: Simplify.
- [tex]x = (0.5)(x) + (0.5)(-3)[/tex]
- [tex]x = 0.5x - 1.5[/tex]
Step 3: Subtract 0.5x from both sides.
- [tex]x - 0.5x = 0.5x - 1.5 - 0.5x[/tex]
- [tex]0.5x = -1.5[/tex]
Step 4: Divide both sides by 0.5.
- [tex]\frac{0.5x}{0.5} = \frac{-1.5}{0.5}[/tex]
- [tex]x = -3[/tex]
Step 5: Check if solution is correct.
- [tex]4^-^3 = 2^-^3^-^3[/tex]
- [tex]\frac{1}{64} = 2^-^6[/tex]
- [tex]\frac{1}{64}=\frac{1}{64}[/tex]
Therefore, x = -3.
