Question

hw 12 solving exponential and logarithmic equations due wednesday by 11:59pm points 100 submitting an external tool solve log₂(x² - 9) - log₂(5) = 3 do not include \x\ in your answer. if there are multiple solutions, separate them with a comma. for example, if you found x = 3 and x = -4 to be solutions, you would enter -4,3. provide your answer below:

Explanation:

Step1: Use log - rule $\log_aM-\log_aN=\log_a\frac{M}{N}$

$\log_2\frac{x^{2}-9}{5}=3$

Step2: Convert log - equation to exponential equation

$\frac{x^{2}-9}{5}=2^{3}$

Step3: Simplify the right - hand side

$\frac{x^{2}-9}{5}=8$

Step4: Multiply both sides by 5

$x^{2}-9 = 40$

Step5: Add 9 to both sides

$x^{2}=49$

Step6: Take square roots of both sides

$x=\pm7$

Answer:

$-7,7$