Question 17 Use the like bases property to solve the equation $$ 7(5)^{n}+10=4385 $$ $$ n=\square $$

Question

UpStudy AI · Accepted Answer

We start with the equation:
$$
7(5)^n + 10 = 4385
$$

**Step 1. Isolate the exponential term:**

Subtract $$10$$ from both sides:
$$
7(5)^n = 4385 - 10 = 4375
$$

Divide both sides by $$7$$:
$$
(5)^n = \frac{4375}{7}
$$

Recognize that $$7 \times 625 = 4375$$, so:
$$
(5)^n = 625
$$

**Step 2. Express $$625$$ as a power of $$5$$:**

Since:
$$
625 = 5^4
$$

We have:
$$
5^n = 5^4
$$

**Step 3. Equate the exponents:**

Since the bases are equal, the exponents must be equal:
$$
n = 4
$$
$$ n = 4 $$

Question 17 Use the like bases property to solve the equation \( 7(5)^{n}+10=4385 \) \( n=\square \)