Question

3*2ˣ⁺¹-2ˣ⁺²+5*2ˣ=21

Answer 1

I hope this helps you

Answer 2

To solve the equation 3 * 2^(x+1) - 2^(x+2) + 5 * 2^x = 21, you can simplify and solve for x step by step.

Let's work through it:

1. First, notice that all terms in the equation have a common base of 2, which is 2^x. We can factor out 2^x from each term:

3 * 2^(x+1) - 2^(x+2) + 5 * 2^x = 21 2^x(3 * 2) - 2^x(2^2) + 5 * 2^x = 21

2. Now, we have the equation in terms of a common base:

6 * 2^x - 4 * 2^x + 5 * 2^x = 21

3. Combine the like terms:

(6 - 4 + 5) * 2^x = 21

9 * 2^x = 21

4. Now, isolate 2^x by dividing both sides by 9:

2^x = 21 / 9

2^x = 7/3

5. To solve for x, you can take the logarithm of both sides. Commonly, the natural logarithm (ln) or base-10 logarithm (log) is used. I'll use the natural logarithm here:

ln(2^x) = ln(7/3)

x * ln(2) = ln(7/3)

6. Now, solve for x by dividing both sides by ln(2):

x = ln(7/3) / ln(2)

You can use a calculator to find the approximate value of x.