Try solving (2 to the x - 1 power) over (2 to the 3 - 4x power) = 16 without a calculator 

John's solution is best but there's a second way to tackle the problem using cross multiplication that does not require knowledge of division of exponents: 2^x-1/2^3-4x = 16/1 2^x-1 = 16(2^3-4x) 2^x-1 = 2^4(2^3-4x) 2^x-1 = 2^4+3-4x 2^x-1 = 2^7-4x x-1 = 7-4x 5x = 8 x = 8/5

A power divided by another power with the same base goes by subtracting both powers, like this: 2^5 : 2^3 = 2^5 - 3 = 2^2 (32 : 8 = 4 and 4 = 2^2). So we can solve this without using logs or whatever, simply by this equation: (X - 1) - (3 - 4 X) = 4 => X -1- 3 + 4X = 4 => 5X = 8 => X = 8/5.

The equation can be rewritten as (2^x/2)/(2^3/2^4x)=16. Which is also (2^x/2)*(2^4x/2^3)=16. This simplifies as 2^5x/2^4=16 or 2^4. Then the equation becomes 2^5x=2^8. Having the same base (2), the exponents are equals so 5x=8 then x=8/5.

To those who complain about the verbosity of the video, he is trying to help those people understand the way to solve problems who might not have had the exposure to the methodology in the past. Just solve the problem and then fast forward to see if you had it right and if not, go back and find out where you failed. If you understand the mathematics, there is no law that you have to "attend" the class.

You can get the right answer to this in your head. The trick is to recognize that 16 is 2^4, so you can just drop the 2^ stuff completely and get a simple linear equation: 2^(x-1) / 2^(3-4*x) = 16 2^(x-1)*2^(4*x-3) = 2^4 x-1+4*x-3 = 4 5*x = 8 x = 8/5 You can actually just read 5*x = 8 right out of the initial equation as given - you don't really need to write down those two intervening lines. If this kind of math is important in your work, then you can't be spending all your time figuring things out - you need to get good enough at it to get "the details" out of your way. Much like how you only get good at a sport or a musical instrument when you make the motions "muscle memory" instead of things you think about. You need to be able to just look at the problem and have most of these steps just happen behind the scenes.

2ˆ(x-1) / 2ˆ(3 - 4x) = 16 => 2ˆ((x-1)-(3-4x)) = 16 => 2ˆ(5x-4) = 16 => 2ˆ(5x-4) = 2ˆ4 => 5x-4 = 4 => 5x = 8 => x = 8/5

Well done. I find in math, there's always that twist to see the answer. In this case, it was to convert the right hand side of the equation to base 2.

I did it using log base 2, but this is a good one too.

X-1-3+4x=4, 5x=8 X=8/5

that was cool. thanks.

8/5, very easy.solved it mentally

First, understanding the properties of exponents and logarithms is essential for doing well in the calculus series. Accordingly, I disagree with John's reasoning, his reasoning about the bases being the same as the justification for equating exponents. I believe one still has to go through the transformation, the transformation for eliminating the base of 2 by using one of the logarithm identities, a step which takes less time than the justification he provided and is easier to write: (x-1)/2^(3-4x)=16 2^((x-1)-(3-4x))=2^4 2^(x-1-3+4x)=2^4 2^(5x-4)=2^4 log2(2^(5x-4))=log2(2^4) (5x-4)log2(2)=4log2(2) Given the logarithm identity loga(a)=1, for all a>0..... (5x-4)(1)=4(1) 5x-4=4 5x-4+4=4+4 5x=8 (5x)/5=(8)/5 x=8/5

Pretty good

a)8/5

Most times you must solve the answer period! There is no time to be plugging in possible answers. Please stop talking so much and show how to solve these problems.

8/5

The answer is 8/5

9

Algebra 1 students will not see this type of problem You see this Algebra 2 and College …You want to pass High School you are going to have to know this Algebra 2 is a high school requirement It wasn’t when I graduated high school in 1976 but it is now I will add you want to have any 4 year degree from college you are going to have to pass college Algebra That is a basic requirement There are many College bound students who test out and don’t have to take college Algebra

I still don't get it 😮

Why are you pronuncing “problem “ in a weird way?

B

x = 8/5

All that talk that you did I still don't understand it cuz you really didn't show us how to do the problem

I'm sorry, it shouldn't have taken 18 minutes to teach a reader these sporoaches to solve this equation. Dies this man just love hearing himself talk?

Way too much talking…

First

too much tym for a simple thing.

Bruh iam 10th grade I solved in 15 second he takes 18 mins for trash problem

8/5

a) 8/5

X =8/5

8/5