Question

solve for $k$.
$2^{k+7}=7$

Explanation:

Step1: Take log base 2 of both sides

$\log_2(2^{k+7}) = \log_2(7)$

Step2: Simplify left side using log property

$k+7 = \log_2(7)$

Step3: Isolate k by subtracting 7

$k = \log_2(7) - 7$

Step4: (Optional) Rewrite log in base 10

$k = \frac{\log(7)}{\log(2)} - 7$

Answer:

$k = \log_2(7) - 7$ or approximately $k \approx -4.19$