Question

1. calculator active: what is the solution to the equation $4 \cdot 2^{x + 5} - 10 = 22$.

Explanation:

Step1: Isolate the exponential term

Add 10 to both sides.
$$4\cdot2^{x+5} - 10 + 10 = 22 + 10$$
$$4\cdot2^{x+5} = 32$$

Step2: Simplify the coefficient

Divide both sides by 4.
$$\frac{4\cdot2^{x+5}}{4} = \frac{32}{4}$$
$$2^{x+5} = 8$$

Step3: Rewrite with same base

Express 8 as $2^3$.
$$2^{x+5} = 2^3$$

Step4: Solve for x

Set exponents equal (same base).
$$x + 5 = 3$$
$$x = 3 - 5$$

Answer:

$x = -2$