Question

3^3x+9*2^2x=4^x+3^2+3x

Answer 1

Ответ: перенеси х в левую часть, без х в правую, потом посчитай, будет по моему ответ 0,9

Объяснение:

Answer 2

To solve the equation $3^{3x} + 9 \cdot 2^{2x} = 4^x + 3^2 + 3x$, we can use algebraic techniques to isolate the variable $x$. Here's the step-by-step process:

Given equation: $3^{3x} + 9 \cdot 2^{2x} = 4^x + 9 + 3x$

Step 1: Express all terms with the same base

Rewrite $9$ as $3^2$ and $2^{2x}$ as $(2^x)^2$:

$3^{3x} + 3^2 \cdot (2^x)^2 = 4^x + 9 + 3x$

Step 2: Simplify the exponents

Apply the exponent properties:

$3^{3x} + 3^4 \cdot 2^{2x} = 4^x + 9 + 3x$

Step 3: Express $3^4$ as $81$

$3^{3x} + 81 \cdot 2^{2x} = 4^x + 9 + 3x$

Step 4: Rewrite $2^{2x}$ as $(2^x)^2$ again

$3^{3x} + 81 \cdot (2^x)^2 = 4^x + 9 + 3x$

Step 5: Apply the exponent property $(a^m)^n = a^{m \cdot n}$

$3^{3x} + 81 \cdot 2^{2x} = 4^x + 9 + 3x$

Step 6: Distribute the exponent in $2^{2x}$

$3^{3x} + 81 \cdot 2^{2x} = 4^x + 9 + 3x$

Step 7: Notice that $81 = 3^4$

$3^{3x} + 3^4 \cdot 2^{2x} = 4^x + 9 + 3x$

Step 8: Apply the exponent properties again

$3^{3x} + 3^{2 + 2x} = 4^x + 9 + 3x$

Step 9: Combine like terms on both sides

$3^{3x} + 3^{2x + 2} = 4^x + 9 + 3x$

Step 10: Express $3^{2x + 2}$ as $\left(3^x\right)^2 \cdot 3^2$

$3^{3x} + \left(3^x\right)^2 \cdot 3^2 = 4^x + 9 + 3x$

Step 11: Simplify the exponents further

$3^{3x} + 3^{2x} \cdot 9 = 4^x + 9 + 3x$

Step 12: Now the equation is in a form where all terms have the same base. Combine like terms.

$3^{3x} + 3^{2x} \cdot 9 = 4^x + 9 + 3x$

Step 13: Express $9$ as $3^2$ 0 0