Question

Solve for x:
log(x+5) + log(x-5) = 4log2 + 2log3
(20 points! :) )​

Answer 1

Answer:

x = 13

Step-by-step explanation:

Given:

log(x + 5) + log(x - 5) = 4 log 2 + 2 log 3

[∵ log a + log b = log ab,  a log b = bᵃ]

⇒ log(x + 5)(x - 5) = log 2⁴ + log 3²

[∵ (a + b)(a - b) = a² - b²]

⇒ log(x² - 5²) = log 2⁴ * log 3²

⇒ log (x² - 25) = log 2⁴ * log 3²

⇒ x² - 25 = 2⁴ * 3²

⇒ x² - 25 = 16 * 9

⇒ x² - 25 = 144

⇒ x² = 169

⇒ x = 13

Hope it helps!