Question

3^(x-1)+18/(3^x)-29=0

Answer 1

3^(x-1)+18/(3^x)-29=0

3^x/3  +18/(3^x)-29=0  умножим на 3*3^x

3^2x-87*3^x+54=0

замена  3^x=t, t больше 0

t^2-87t+54=0  перепроверь уравнение получается некрасивый Д

Answer 2

To solve the equation 3^(x-1) + 18/(3^x) - 29 = 0, we can simplify it by combining like terms and manipulating the equation algebraically. Here's how:

Let's start by multiplying the entire equation by 3^x to eliminate the fractions:

3^x * 3^(x-1) + 3^x * (18/(3^x)) - 3^x * 29 = 0

Now, simplify each term:

3^(2x-1) + 18 - 29 * 3^x = 0

Next, move the constant term (18) to the right side of the equation:

3^(2x-1) = 29 * 3^x - 18

We can rewrite 29 as 3^1 * 3^x and 18 as 3^2:

3^(2x-1) = 3^(x+1) * 3^x - 3^2

Now, using the property of exponents that states a^m * a^n = a^(m+n), we can simplify further:

3^(2x-1) = 3^(2x) - 3^2

Since the bases are the same (3), we can equate the exponents:

2x - 1 = 2x - 2

Now, we can solve for x:

2x - 2x = -2 + 1

0 = -1

The equation 0 = -1 is not true, which means there is no solution to this equation. Therefore, the original equation 3^(x-1) + 18/(3^x) - 29 = 0 has no solution.