Q:

Solve for x: log(3x) + log(x + 4) = log(15).

Accepted Solution

A:
Answer:The solutions are x = 1 and x = -5Step-by-step explanation:Hi there!First, let´s write the equation:log(3x) + log(x + 4) = log(15)Apply logarithm property: log(3x) = log(3) + log(x)log(3) + log(x) + log(x + 4) = log(15)Substract log(3) from both sides of the equationlog(x) + log(x+4) = log(15) - log(3)Apply logarithm property: log(15) - log(3) = log(15/3) = log(5)log(x) + log(x + 4) = log(5)Apply logarithm property: log(x) + log(x+4) = log(x (x+4)) = log(x² + 4x)log(x² + 4x) = log(5)Apply logarithm equality rule: if log(x² + 4x) = log(5), then x² + 4x = 5 x² + 4x = 5 Substract 5 from both sidesx² + 4x - 5 = 0Using the quadratic formula (a = 1, b = 4, c = -5)x = 1 and x = -5The solutions are x = 1 and x = -5Have a nice day!