5/3 did mentally in less than 10 seconds. Too easy, but it’s refreshing to see a video about an equation on RU-vid that does not involve the Lambert W function in the solution.
And I'm like a jerk instead of 8^x=32 => 2^3x = 2^5 for some reason I went this way: 8^x = 8 * 4, then 4^x * 2^x = 8* 4, divided by 4... and so on... well, I did not notice that you can do 8^x = 2^3x at once, and 32 = 2^5 (It's all a translator, if there are mistakes here!!
@@normalstranger6482 You had the same approach as the video essentially!.. just needed to use log base 2 instead of log base 10. 8^x = 32 log (8^x) = log(32) x * log(8) = log(32) x *log(8)/log(2) = log(32)/log(2) x * logbase2(8) = logbase2(32) x * 3 = 5 x = 5/3 (or just use log2 right away)
Which would be .. let me get a calculator . 1.6~ power. Which while I don't have the faculty to do 1.6 power in my head. It would be 166.66666666% power Which helps. So its 5.333333333 repeating over the number. That would give us 8. 8^1 = 8 8^2 = 64 A quick calculation would give us a miscalculation That being half of 64 is 32 So we would think 1.5 But this is exponents between 1 and 2 We have a number that gives us 4 Exponentially 8×1 =8 8*8 = 64 1-8 valued to get 4 is a 66% difference 2-7 Being directly at the 1/2 mark. Which is why the 66% exponent is needed.
@user-tc9di5wf7x nope. 8^x is getting multiplied by 2 and then the whole thing is divided by 2. We can see it as this: we get into a car, I move it 2 meter forward and then 2 meters back, we just reached where we were so the 2s cancel out leaving 8^x only
@@bilaalahmed8923 not the greatest explanation. What you said would represent addition/subtraction. A much better explanation would be a colony of bacteria doubles instantaneously and then half of the new colony are killed in sanitation
