When and how to use Log

[xdragonk]

I just noticed that he uses projector to project the question to the blackboard.

[leo_jay]

Take log of both sides. Log(a^x) = xlog(a)
xlog(3) = log(10)
x = log(10) / log(3) = 2.09....

[TeacherLisaHello]

Mr H knows how to do all the Maths in most efficient of ways!!! Super cool!!

[coloradowestaerialarts]

I am really enjoying this channel; working on problems right away.

[geopad]

I like you simple but elegant explanation

[sedgarmath]

We teach students to treat the LHS and the RHS the same just take the log(base 3) of both sides. I am not sure why we don't extend this when dealing with logarithms. But THIS is how I was taught as well.

[jonathanljohnson]

I could never catch on to calculus, because no one ever explained this definition so clearly to me.

[AgMak]

You look way better with a beard like this, may Allāh guide you to Islām

[kennethkossan]

I absolutely love the stuff. It completely brings me back to algebra class and I love doing man I miss it. I miss doing it what I want to do is at age 57 go back and start taking some physics classes so I can start applying the man Solving real life problems with math I learned in math class I ended up in art school, but I really love science. I adore it and I adore math

[kirkisdad]

You are awesome!!!! Very good teacher!

[ProtectFreedomOfSpeech]

I absolute hate math and I finished with school a few years ago but you make me want to give it another go and resolve that hatred towards it :)

[lordbeansofmemes]

Literally been learning this in school for the past week or so

[zedzedder]

I think I should refresh my knowledge. I completely forgot this.

[scottwebster]

it always seemed like a shell game to me.
watch as the 3 and the 10 move like someone is asking you to guess where the x is.

[Rayleigh]

How can we solve this without calculator 😊

[philh]

Have you made a video on how to do a log manually without a calculator?

[aimranehd]

i learnt this in school not so long ago.
here's my understanding:
3^x = 10
log_3(3^x) = log_3(10)
x•log_3(3) = log_3(10)
x•(ln(3) ÷ ln(3)) = log_3(10)
x•1 = log_3(10)
x = log_3(10)

the property used:
- log_a(x) = ln(x) ÷ ln(a)
- ln(x^n) = n•ln(x) (same thing with log())

[dono]

Are there any calculators with a base-3 log button? Sure you can change the base, but it easier to just... 1) take log (any base available) on both sides, 2) drop the exponent down, and finally 3) divide by log 3 to get x alone. Hence, x = log 10 / log 3.

[chantinghang]

Just a reminder, x can be -2 when 3^x=9

[aj___plays]

We can directly put that equation in calculator 😅