1 over 12 to the 2x power = 12, Many will not where to start to solve this equation…

[@joevincente3004]

It's good to see his looks is equal to his voice. Now that's a balanced equation. Lol

[@rpinter677]

Good lesson!

[@joyce_915]

Thank You!

[@juergenilse3259]

Since 1/a is the same as a^(-1) for every number for which 1/a is defined (it is undefined for n=0), we can rewrite 1/12^2x as (12^2x)^(-2). We can rewrite this to 12^(-2x), because of the rule (a^n)^m=a^(n*m). (12^2x)^-1=12^((-1)*2x)=12^-2x. If we insert the equation 1/12^2x=12^(-2x) in the equation, we get: 12^(-2x)=12 Since 12 is the same as 12^1, we have powers of 12 on both sides of the equation: 12^(-2x)=12^1 -For bases different from 0 and different from 1, the equation b^n=b^m is fullfilled if and only if n=m, so we get -2x=1 2x=-1 x=-1/2 That is the solution. We don't need to check the result, because we did no transformation that may have added additional errnous solutions.

[@joyce_915]

I love your teaching style. This is why I subscribed 😊 Personal goals. 😊

[@russelllomando8460]

great lesson, thanks the - will flip the equation.

[@terry_willis]

I guessed (solved) this in about 6 seconds. Since the fraction would give you less value than 12 (actually less than 1), the exponent HAS to be negative (to flip the fraction and become positive). Then simple observation forces x to be -1/2 to yield net exponent of 1. Easy peasy.

[@chrisdissanayake6979]

Answer: 1 x = - - 2 ----------- 1 -- = 12 12^2x Let’s see how we can 1 make --- equal to 12 12^2x The rule for negative exponents states that 1 a^-2 = -- a^2 1 1 12^-1 = -- = -- 12^1 12 1 Then, -- = 12 12^-1 That means, 2x = -1 1 Therefore, x = - - 2

[@josephlaura7387]

X=-1/2

[@stevendebettencourt7651]

Huh, well, this is one that looks tricky at first, but is rather simple when you break it down. Let’s go! 1 / (12^(2x)) = 12 So there are two ways to go about this. The first is to remember that: a^(-x) = 1 / (a^x) Using this, we can rewrite this as: 1 / (12^(2x)) = 12^(-2x) = 12 = 12^1 Since we now have an equation in the form of a^b = a^c, we know that b = c. So, -2x = 1 x = -1/2 There is a second way I want to try, but it requires more math. Let’s do this: 1 / (12^(2x)) = 12 1 = 12 * (12^(2x)) 12^(2x) = 1/12 Now, I am gonna take log base 12 of both sides (why 12? You’ll see in a sec): Log_12 (12^(2x)) = log_12 (1/12) Remember our log rules, I’ll list the two we need: Log (a^b) = b log (a) Log (a/b) = log (a) - log (b) With these in mind: (2x) log_12 (12) = log_12 (1) - log_12 (12) And now these log identities: Log_a (1) = 0 Log_a (a) = 1 And now you see why I chose base 12. Also, base 12 is the master base, superior to base 10 in all ways: (2x)(1) = 0 - 1 2x = -1 x = -1/2 And there you go, same answer via two paths.

[@Stylux-z1p]

well, well I see some twelves some rules : 1/a = a^-1 , a^(1/2) = √a, (a³)² = a^(3 x 2) = a^6 1/12^(2x) = 12 (12^(2x))^-1 = 12 12^(-2x) = 12^1 Equality Property of Exponents -2x = 1 -2x/-2 = 1/-2 x = -1/2✅ proof : substitute the value of x = -1/2 in the equation 1/12^(2(-1/2) = 12 1/12^(-1) = 12 12 = 12 matched

[@panlomito]

1 = 12 . 12^2x = 12^(2x+1) 12^0 = 1 so 2x+1 = 0 and x = -½ Check: 12^(-2.-½) = 12^1 = 12 tadaaa !

[@George50809]

x = -1/2. A smiley face.

[@Gratitude24th]

Thank u

[@laurendoe168]

12^(-2x) = 12^1 therefore -2x = 1 x = -1/2

[@cyruschang1904]

1/12^(2x) = 12 12^(2x + 1) = 1 2x + 1 = 0 x = -1/2

[@giannaleoci2328]

12^(-2x)=12 -2x=1 x=-1/2

[@samcarrillo8608]

X=0

[@AC34D]

(-1/2)=x

[@Mountainlion-d5h3c]

Dolled it in my head. Answer is -.5

[@b213videoz]

12-²× = 12¹ -2x = 1 x = -½

[@fofanamusa3331]

X= 1/2

[@BrenoStrato]

x = - 1/2.

[@subasu478]

-1/2

[@shanedal]

X=--1/2

[@aek03030731]

An awfully complicated solution to a straightforward problem. Since 1/12^2x=12, then 12^2x=1/12. If one knows how negative exponents work, one knows that 1/12 can be expressed as 12^-1: hence, 2x=-1, x= -1÷2 = -½.

[@PYTHAGORAS101]

MINUS one half is the more correct expression. Negative numbers do not actually exist, they are a type of theoretical abstraction that has no place in algebraic arithmetic's. Prove me wrong. The ultimate expression, to me at least, is minus point five because it resolves the fraction.

[@erniemorris9991]

You typed absolute NONSENSE

[@PYTHAGORAS101]

@@erniemorris9991 Decades ago, I may have agreed with you. What i am saying is not mainstream understanding so I know why you feel that way. Numbers are my passion and hobby, and I have learned to understand their properties and laws. It is not man's business to be inventing new numbers with new properties. We are supposed to learn the properties and obey number laws. Negatives, Imaginaries, complex and also zero and infinity are inventions, known as theoretical abstractions and they are illegitimate so-called" numbers". They are for pseudoscience and are totally useless in the real world.

[@EricWells-s2p]

x = -1/2

[@sydrider6023]

-1/2

[@danielmadden9691]

-1/2

[@randallheisey3698]

X=-1/2

[@EricWells-s2p]

x = -1/2