It's the opposite of exponenciation, your x in a logarithm is the exponent you need to give to the base (10 in this case) so that the result is equal to 80 (which is called the argument I think). Not that hard to grasp as a concept
A video about a list of the usual "tricks" that can be used in such math problems (like the 30-60-90 triangle, the exponent substitutions you used here, etc...) would be amazing! Thanks!
I’m having flashbacks to helping my daughter with Algebra 2 😮 I love how you manage to keep the presentation so brisk, yet also don’t have any mystery steps.
I tried solving it before the video, ended up with the same answer. I just did the log base 2 of 40 first to get the exponent bases to 2. got something around 5.32. set the exponents = to each other due to same bases and boom basic algebra to get to the same decimal answer. (with calculator ofc) nice video tho man 👍
Before even watching the video I know I'm gonna hear "Lets put a box around it" and "How exciting". Almost forgot the “Nice” every time 69 or 420 shows up. And you can’t forget the “this looks like a fun problem” when the video starts.
My math teacher in high school wouldn't have allowed log 80 as an answer because it can be reduced like square root of 80 can be reduced. Because it is base 10, log 80 = log 10 + log 8 since log ab = log a + log b if the base is the same. Log 10 = 1, so log 80 = 1+ log 8.
Depends, sometimes it’s the opposite. With a class that I was in, they would want me to write 1 + log 8 as log 80. But log 8 on its own would need to be simplified to 3log 2.
i did it by applying log to both sides, and then solving. it makes it easier because after that its just manipulation. but you do need the value for log 2 and log 40.
2:31 I think explaining that with the inverse function is more logical. Just like in _tan x = 2_ we take the inverse function of _tan_ on both sides, which is _tan^-1_ that gives us _tan^-1 (tan x) = tan^-1 (2)_ which simplifies to _x = tan^-1 (2)_ Here, the inverse function of _10^x_ is _log 10 (x)_ Taking that on both sides gives us _log 10 (10^x) = log 10 (80)_ which simplifies to _x = log 10 (80)_
I knew that because I brute forced and put 1 as x and 2 as x and then just did 1.5 and kept raising it to 1.9.... They need to make it a bigger x so that I can't just input numbers quicker than it takes to actually use the correct formulas😅
Easy method here Just take log on both sides and multiply it in side then you should have an equation with both sides having x of power one and substitute values of log40 ( log4 +log10) and log 2 Then u get 1.602x-1.602=0.601x+0.301 On bringing x oneside and constant on other side u get 1.001x=1.903 Which is approx answer x=1.903 If you need more precise then increase the decimal numbers That's it not even a 2min task
That's what i was thinking it took me about 1 min to solve this mentally i was like he must have asked a numerical value i solved log 8 ans 3log2 = 3X.30 and i got 1.90
@@rathersane You can use logarithm regardless but yes, it's usually 10 as base. In this case, it works better. I'm just saying what I prefer in my opinion. Is that bad?
just introduce logs to both sides in the beginning 40^x-1=2^2x+1 log 40^x-1= log 2^2x+1 power law of logs, the power of the log can become the coefficient of the log (x-1) log 40 = (2x+1) log 2 x log40 - log40 = 2x log2 + log2 move the x terms to the left, and the log40 to the right x log40 - 2x log2 = log 2 + log 40 factorise x from the right x(log 40 -2log2) = log2 + log40 x= (log2 + log40) / (log40 -2log2) = 1.903089987
so simple you just know about log 5on2 =2.3 and done and solve it but you can do it simple you should change this log to log5 /log2 => 0.7/0.3 =2.3 (rounded ) and you dont wana calculator or somthing this question was standard for student
pls do more about shapes and derivation i had a question asking what is the biggest [ pyramid ] i can fit inside a cylinder pls help me solving something like this i love ur vidsss💓💞😭
problem solving is a very important transferable skill. Being good at solving any math problem means your likely a good problem solver in any setting. Yes, you won't need to solve this specific equation or anything like this in a practical setting, but it trains your brain to think outside the box
It’s an exponential function. You can google the purpose and application of those. This is a problem solving channel, not an application and vague question answering channel.
From 1st sec, i striaght knows that just using ln() then find the x. Just that simple. No need to be simplify🤔 why need sinplify as we can just using ln() loll
