Question

Solve the logarithmic equation. When necessary, round answer to the nearest hundredth. log 3(x + 4) - log 3(x + 2) = log 327

Answer 1

Answer:

$x = -\dfrac{25}{13}$

Step-by-step explanation:

$\log_3{x + 4} - \log_3{x + 2} = \log_3 {27}$

$\log_3 \dfrac{x + 4}{x + 2} = \log_3 {27}$

$\dfrac{x + 4}{x + 2} = 27$

$x + 4 = 27(x + 2)$

$x + 4 = 27x + 54$

$-26x = 50$

$x = -\dfrac{50}{26}$

$x = -\dfrac{25}{13}$