Question

3^x+2=9^x+1

Answer 1

Ответ:

1) 60

2) =~0,43

Иррациональные выражения.

Answer 2

To solve the equation $3^{x+2} = 9^{x+1}$, you can use the fact that $9$ is equal to $3^2$. This allows you to rewrite the equation as follows:

$$3^{x+2} = (3^2)^{x+1}$$

Now, apply the properties of exponents, specifically the rule that states $(a^b)^c = a^{b \cdot c}$. In this case, $a = 3$, $b = 2$, and $c = x+1$:

$$3^{x+2} = 3^{2(x+1)}$$

Since the bases are the same (both $3$), you can equate the exponents:

$$x+2 = 2(x+1)$$

Now, solve for $x$:

Expand the right side:

$$x+2 = 2x+2$$

Subtract $2x$ from both sides:

$$2 - x = 2$$

Subtract $2$ from both sides:

$$-x = 0$$

Now, multiply both sides by $-1$ to isolate $x$:

$$x = 0$$

So, the solution to the equation $3^{x+2} = 9^{x+1}$ is $x = 0$.