# SOLUTION: I have a couple of questions that I need help with: 1. Solve for x: ln7 + ln(x-3) = ln(x + 15) 2. Solve for x: 28 = 19 + 12^(x-7) **The (x-7) is an exp

Algebra ->  Algebra  -> Logarithm Solvers, Trainers and Word Problems -> SOLUTION: I have a couple of questions that I need help with: 1. Solve for x: ln7 + ln(x-3) = ln(x + 15) 2. Solve for x: 28 = 19 + 12^(x-7) **The (x-7) is an exp      Log On

 Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations! Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!

 Algebra: Logarithm Solvers Lessons Answers archive Quiz In Depth

 Question 4694: I have a couple of questions that I need help with: 1. Solve for x: ln7 + ln(x-3) = ln(x + 15) 2. Solve for x: 28 = 19 + 12^(x-7) **The (x-7) is an exponent for the number 12 3. Solve for x: e^(3x-4) = 1/e^(x-12) **The (3x-4) and (x-12) are both exponents 4. Use the properties of logarithms to write 3lnx^2 + ln(2x-4)-ln(3x-6) as a single logarithm. To whoever is kind enough to help with answering these problems: Thank you and I would appreciate it if you could show your work so I can better understand how to do these types of problems myself. Thanks again!Found 2 solutions by rapaljer, longjonsilver:Answer by rapaljer(4667)   (Show Source): You can put this solution on YOUR website!1. ln7 + ln(x-3) = ln(x + 15) First get the variables on one side (the right side) by subtracting ln(x-3) from each side. ln 7 = ln(x+15) - ln(x-3) Use the property of logs to express the right side as a log of a single quantity: Because ln A = ln B, you can say that A=B. In the same way, Multiply both sides of the equation by (x-3): Check to make sure x= 6 doesn't give you the log of a negative. It does not. 2. Subtract 19 from each side of the equation: Take the ln of each side: By law of logarithms: By distributive property: Add 7 ln (12) to each side: Divide both sides by ln (12) I'm very sorry, that's all I have time for. Maybe someone else will do the others, or perhaps you can repost them. R^2 at SCC Answer by longjonsilver(2297)   (Show Source): You can put this solution on YOUR website!1. . Now just raise everything to the power e, to remove the natural logs: 7(x-3) = x+15 7x-21 = x+15 6x = 36 x = 6 2. . Take logs to the base 10: x-7 = 0.884228 so x = 7.884228 3. . Now take natural logs of both sides, to remove the "e": 3x-4 = 12-x 4x = 16 x = 4 --> check these answers in the original questions. jon.