Question

4*3^x+2+5*3^x+1-6*3^x=5 Решите неравенство

Answer 1

пусть у=3^x  тогда  4у+2+5у+1-6у=5  3у+3=5 3у=2 у=2/3   3^x=2/3

Answer 2

To solve the inequality, we need to find the value(s) of 'x' that satisfy the given equation. Let's simplify the equation and then solve for 'x':

We have: 4 * 3^x + 2 + 5 * 3^(x+1) - 6 * 3^x = 5

First, let's simplify the terms with 3^x and 3^(x+1):

5 * 3^(x+1) can be rewritten as 5 * 3^x * 3^1, which is equal to 5 * 3 * 3^x, or 15 * 3^x.

Now our equation becomes: 4 * 3^x + 2 + 15 * 3^x - 6 * 3^x = 5

Combine the terms with 3^x:

(4 + 15 - 6) * 3^x + 2 = 5

Now simplify further:

13 * 3^x + 2 = 5

Subtract 2 from both sides:

13 * 3^x = 3

Now, to solve for 'x', we need to isolate the term with 3^x. Divide both sides by 13:

3^x = 3/13

To solve for 'x', we'll take the logarithm of both sides. Let's use the natural logarithm (ln) for convenience:

ln(3^x) = ln(3/13)

Now, we can use the property of logarithms that states: ln(a^b) = b * ln(a)

x * ln(3) = ln(3/13)

Finally, solve for 'x':

x = ln(3/13) / ln(3)

Using a calculator:

x ≈ -1.391

So, the solution to the inequality is approximately x < -1.391.