Use the like bases property to solve the equation $$ 5^{n}=625 $$ $$ n=\square $$

Question

UpStudy AI · Accepted Answer

To solve the equation $$ 5^{n} = 625 $$ using the like bases property, we first express $$ 625 $$ as a power of $$ 5 $$.

1. **Identify the base**: The base on the left side of the equation is $$ 5 $$.

2. **Express $$ 625 $$ as a power of $$ 5 $$**:
   - We know that $$ 625 = 5^4 $$ because $$ 5 \times 5 \times 5 \times 5 = 625 $$.

3. **Rewrite the equation**:
   - Now we can rewrite the equation as:
   $$
   5^{n} = 5^{4}
   $$

4. **Set the exponents equal to each other**:
   - Since the bases are the same, we can set the exponents equal:
   $$
   n = 4
   $$

Thus, the solution to the equation is:
$$
n = 4
$$
$$ n = 4 $$

Use the like bases property to solve the equation \( 5^{n}=625 \) \( n=\square \)