Question

8^x -3*4^x+1 -2^x+2 +48=0

Answer 1

$8^x-3*4^{x+1}-2^{x+2}+48=0$

$8^x-3*4*4^x-4*2^x+48=0$

$2^{3x}-12*2^{2x}-4*2^x+48=0$

$2^x(2^{2x}-4)-12(2^{2x}-4)=0$

$(2^x-12)*(4^x-4)=0\\x1=1\\x2=log2(12)$

Answer 2

$8^{x}-3\cdot 4^{x+1}-2^{x+2}+48=0\\\\2^{3x}-12\cdot 2^{2x}-4\cdot 2^{x}+48=0\\\\t=2^{x}>0\; \; ,\; \; t^3-12t^2-4t+48=0\; ,\\\\(t^3-4t)-(12t^2-48)=0\\\\t\, (t^2-4)-12(t^2-4)=0\\\\(t^2-4)(t-12)=0\\\\a)\; \; t^{2}=4\; \; ,\; \; t=\pm 2\; \; \Rightarrow \; \; 2^{x}=2>0\; \; ,\; \; x=1\\\\b)\; \; t=12\; \; ,\; \; 2^{x}=12\; \; \Rightarrow \; \; x=log_212=2+log_23\\\\Otvet:\; \; x=1\; ,\; x=2+log_23\; .$

Answer 3

To solve the equation $8^x - 3 \cdot 4^x + 1 - 2^x + 2 + 48 = 0$, we'll simplify the terms step by step.

1. Notice that $8 = 2^3$ and $4 = 2^2$. So, we can rewrite the equation as:

$(2^3)^x - 3 \cdot (2^2)^x + 1 - 2^x + 2 + 48 = 0$

2. Now, apply the rules of exponents:

$2^(3x) - 3 \cdot 2^(2x) + 1 - 2^x + 2 + 48 = 0$

3. Combine like terms:

$2^(3x) - 3 \cdot 2^(2x) - 2^x + 51 = 0$

4. The equation cannot be simplified further. At this point, you can try solving for $x$ numerically using methods like iterative techniques or graphical methods. Alternatively, you can use numerical solvers available in software like Python or MATLAB to find approximate solutions.

If you were looking for a specific value of $x$ or any further instructions, please let me know, and I'll be happy to assist further!