IB`NOT`ez Posted July 1, 2016 Report Share Posted July 1, 2016 Hello, I found a question on my Haese Maths SL Textbook I couldn't solve regarding exponentials: Solve for x in 12*3^-x = 4/3 What I first did was multiply everything by 3: 3(12*3^-x) = 4 -> 36*3^-x+1 = 4. Then I divided the 4 by 36, which simplifies to 1/9: 3^-x+1 = 4/36 -> 3^-x+1 = 1/9 1/9 is the same as 1/3^2 = 3^-2, thus the equation becomes: 3^-x+1 = 3^-2 Since we have equal bases: -x + 1 = -2 -> -x = -3 -> x = 3 Thus I found x = 3. However, in the answers section of the textbook, it states that x = 2. How do I get x = 2? Is there a step/concept I'm misunderstanding as I've redid the problem 3 times now still with no avail. Thanks, appreciate any help! Reply Link to post Share on other sites More sharing options...
kw0573 Posted July 1, 2016 Report Share Posted July 1, 2016 (edited) 10 hours ago, IB`ez said: What I first did was multiply everything by 3: 3(12*3^-x) = 4 -> 36*3^-x+1 = 4. In the first step, you actually multiplied the left side by 9 and right side by 3. You did 3 * (12 *( 3-x * 31)) when really that's 3 * 31 * 12 * 3-x = 9*12*3-x by the commutative and associative properties. Quote Commutative Property of Multiplication: ab = ba Associative Property of Multiplication: abc = (ab)c = a(bc) You only multiply both sides for each terms that are added or subtracted. In the question, 12(3-x) is a single term, so you only multiply by 3 once. For example, if the question had been instead 12 + 3-x then there would have been 2 terms, and when you multiply by 3, you would have correctly done 36 + 3-x+1. Edited July 1, 2016 by kw0573 oops messed up on the exactly what the properties are Reply Link to post Share on other sites More sharing options...
IB`NOT`ez Posted July 1, 2016 Author Report Share Posted July 1, 2016 50 minutes ago, kw0573 said: In the first step, you actually multiplied the left side by 9 and right side by 3. You did 3 * (12 *( 3-x * 31)) when really that's 3 * 31 * 12 * 3-x = 9*12*3-x by the commutative property. You only multiply both sides for each terms that are added or subtracted. In the question, 12(3-x) is a single term, so you only multiply by 3 once. For example, if the question had been instead 12 + 3-x then there would have been 2 terms, and when you multiply by 3, you would have correctly done 36 + 3-x+1. Holy crap I got x = now! Thanks so much for clarifying that; I feel silly that mistakes like those keep popping up everywhere in both exams and practices. Really appreciate the help! 1 Reply Link to post Share on other sites More sharing options...
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