Question

4^(3-2x) - 2^(4-2x) =0

Answer 1

$4^{3-2x}-2^{4-2x}=0,$

$2^{6-4x} -2^{4-2x} =0,$

$6-4x=4-2x,$

$-2x=-2,$

$x=1$

Ответ: 1

Answer 2

To solve the equation $4^{3-2x} - 2^{4-2x} = 0$, we can use logarithms to simplify the exponents and solve for $x$. Here's the step-by-step solution:

Step 1: Express both terms with the same base (let's choose $2$): $4^{3-2x} = (2^2)^{3-2x} = 2^{2(3-2x)} = 2^{6-4x}$ $2^{4-2x} = 2^4 \cdot 2^{-2x} = 16 \cdot 2^{-2x} = 2^{4} \cdot 2^{-2x} = 2^{4-2x}$

Step 2: Set the exponents equal to each other since the bases are the same: $2^{6-4x} = 2^{4-2x}$

Step 3: Since the bases are equal, the exponents must also be equal: $6-4x = 4-2x$

Step 4: Now, solve for $x$: Subtract $4$ from both sides: $6-4x - 4 = 4-2x - 4$ $2-4x = -2x$

Step 5: Move all terms with $x$ to one side of the equation: $2-4x + 2x = -2x + 2x$ $2-2x = 0$

Step 6: Move the constant term to the other side: $2-2x - 2 = 0 - 2$ $-2x = -2$

Step 7: Finally, solve for $x$: $x = \frac{-2}{-2}$ $x = 1$

So, the solution to the equation is $x = 1$.