solve the logarithmic equation algebraically. Approximate the result to the three decimal place. 1n(2x+7)-1n(x-5)=1n(x-6)

x = 10.887 or 2.113

Explanation:

ln(2x+7) - ln(x-5) = ln(x-6)

ln[(2x+7)/(x-5)] = ln(x-6)

(2x+7)/(x-5) = x-6

2x+7 = (x-6)(x-5)

2x+7 = x^2 -11x + 30

x^2 -13x +23 = 0

x = [13 ± √(169-4*23)]/2

x = [13 ± √77]/2

x = [13 ± 8.774]/2

x = (13 + 8.774)/2 or (13 - 8.774)/2

x = 10.887 or 2.113

answer: 100

step-by-step explanation: