Question

4^x+2 - 4^x+1 + 4^x=39

Answer 1

Ответ:

x=1/2 * log₂(3) или x≈0.792481

Пошаговое объяснение:

(4²-4+1) * 4ˣ=39

(16-4+1) * 4ˣ=39

13 * 4ˣ=39

4ˣ=3

x=1/2 * log₂(3) или x≈0.792481

Answer 2

To solve the equation $4^{x+2} - 4^{x+1} + 4^x = 39$, we can start by simplifying the terms with the same base, which is 4 in this case. Recall that $a^{m+n} = a^m \cdot a^n$ and $a^{m-n} = \frac{a^m}{a^n}$. Using these rules, we can simplify the equation step by step:

$$4^{x+2} - 4^{x+1} + 4^x = 39$$

First, we can express $4^{x+2}$ as $4^x \cdot 4^2 = 16 \cdot 4^x$ and $4^{x+1}$ as $4^x \cdot 4^1 = 4 \cdot 4^x$:

$$16 \cdot 4^x - 4 \cdot 4^x + 4^x = 39$$

Now, we have all terms with the same base (4^x), so we can combine them:

$$(16 - 4 + 1) \cdot 4^x = 39$$

Simplify the coefficients:

$$13 \cdot 4^x = 39$$

Now, divide both sides by 13:

$$4^x = \frac{39}{13}$$

Simplify the right side:

$$4^x = 3$$

Now, to solve for $x$, you can take the logarithm of both sides. You can use the natural logarithm (ln) or base-10 logarithm (log) depending on your preference:

Using the natural logarithm (ln):

$$ln(4^x) = ln(3)$$

Apply the power rule of logarithms (ln(a^b) = b * ln(a)):

$$x * ln(4) = ln(3)$$

Now, divide both sides by ln(4) to isolate x:

$$x = \frac{ln(3)}{ln(4)}$$

Using base-10 logarithm (log):

$$log(4^x) = log(3)$$

Again, apply the power rule of logarithms (log(a^b) = b * log(a)):

$$x * log(4) = log(3)$$

Divide both sides by log(4) to isolate x:

$$x = \frac{log(3)}{log(4)}$$

You can calculate the numerical value of $x$ using either of these equations and a calculator.