Question 5 Use the like bases property to solve the equation $$ 5^{n+7}=5^{6 n-9} $$ $$ n= $$ Question Help: Video Submit Question

Question

UpStudy AI · Accepted Answer

1. Given the equation:
   $$
   5^{n+7} = 5^{6n-9}
   $$

2. Since the bases are the same, the exponents must be equal:
   $$
   n+7 = 6n-9
   $$

3. Solve for $$ n $$:

- Subtract $$ n $$ from both sides:
     $$
     7 = 5n - 9
     $$
   
   - Add $$ 9 $$ to both sides:
     $$
     16 = 5n
     $$

- Divide both sides by $$ 5 $$:
     $$
     n = \frac{16}{5}
     $$

4. Therefore, the solution is:
   $$
   n = \frac{16}{5}
   $$
$$ n = \frac{16}{5} $$

Question 5 Use the like bases property to solve the equation \( 5^{n+7}=5^{6 n-9} \) \( n= \) Question Help: Video Submit Question