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Exponentials Question help!

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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! 

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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 by kw0573
oops messed up on the exactly what the properties are

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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! :) 

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