Question

13^2x+3:13^4x-11=169

Answer 1

132x+3/13–4x–11=132x+3·134x+11=132x+3+4x+11=136x+14

136x+14=132

6x+14=2

6x=2–14

6x=–12

x=–2

О т в е т. –2

Answer 2

Ответ:

Пошаговое объяснение:

Answer 3

To solve the equation $13^{2x+3} : 13^{4x-11} = 169$, we'll start by simplifying the left-hand side of the equation using the properties of exponents.

Remember that $a^m : a^n = a^{m-n}$ for any nonzero value of $a$. We can apply this property to simplify the equation.

Let's simplify the left-hand side of the equation first:

$13^{2x+3} : 13^{4x-11} = 13^{(2x + 3) - (4x - 11)} = 13^{2x + 3 - 4x + 11} = 13^{14 - 2x}$

Now, our equation becomes:

$13^{14 - 2x} = 169$

To solve for $x$, we need to find the value of $x$ that satisfies the equation.

Next, we can rewrite both sides of the equation with the same base (13) and then equate the exponents:

$13^{14 - 2x} = 13^2$

Since the bases are the same, we can equate the exponents:

$14 - 2x = 2$

Now, let's solve for $x$:

$14 - 2x = 2$

Subtract 14 from both sides:

$-2x = 2 - 14 = -12$

Divide by -2:

$x = \frac{-12}{-2} = 6$

So the solution to the equation is $x = 6$.