(d) If $$ 2^{15}=4 imes 2^{n} $$, solve for $$ n $$

Question

(d) If $$ 2^{15}=4 	imes 2^{n} $$, solve for $$ n $$

UpStudy AI · Accepted Answer

1. Rewrite the equation using the identity $$4 = 2^2$$:
   $$
   2^{15} = 2^2 \times 2^{n}
   $$

2. Combine the exponents on the right side using the rule $$2^a \times 2^b = 2^{a+b}$$:
   $$
   2^{15} = 2^{n+2}
   $$

3. Since the bases are equal, set the exponents equal:
   $$
   15 = n + 2
   $$

4. Solve for $$n$$:
   $$
   n = 15 - 2 = 13
   $$

The solution is $$ n = 13 $$.
$$ n = 13 $$

(d) If , solve for