Use the like bases property to solve the equation $$ 7(2)^{n}=56 $$ $$ n=\square $$

Question

UpStudy AI · Accepted Answer

1. Start with the equation:
   
   $$
   7(2)^n = 56
   $$

2. Divide both sides by $$ 7 $$ to isolate the exponential term:

$$
   (2)^n = \frac{56}{7} = 8
   $$

3. Express $$ 8 $$ as a power of $$ 2 $$:

$$
   8 = 2^3
   $$

4. Now the equation becomes:

$$
   2^n = 2^3
   $$

5. Since the bases are the same, equate the exponents:

$$
   n = 3
   $$

Thus, $$ n = 3 $$.
$$ n = 3 $$

Use the like bases property to solve the equation \( 7(2)^{n}=56 \) \( n=\square \)