Solving Log Equation with Different Bases

[neilmorrone]

Yes indeed! One does learn something New everyday. I was unfamiliar with this manipulation of Log bases, or at least not consciously remembering.
Sincerely, Thank you, again!

[cebelihlenxumalo]

you have given me clue on how to deal with log equations, as we are about to proceed dealing with them at school, thank you very much sir ❤

[lizzybach]

A better version of this rule can be written as:

Logb^n(a^m) = (m/n)logb(a).

If m=n=2, you'll get the rule that this sir mentioned here.

[luisclementeortegasegovia]

Excelent algorithm 👍
Thanks professor

[altpersonas]

I just failed a test on logarithms today…. Why did this have to come on my feed NOW 😭

[bytemark]

Another way of working out the solution is by going all the way up to eliminating the logs out and at the (x+1)^2 = 3x + 3 => (x+1)^2 = 3(x+1) => and now, we can simplify by (x+1), but that means that x cannot be -1, because we can't simplify by 0, so the only thing that's left is x+1 = 3, or x=2

[abhisheksaxena]

Wow i didnt know this rule in log thanks for this knowledge ❤

[zahariastoianovici]

Did not know this rule, this is nice!

[Nothingx]

But what about the base changing formula? Ik this rule was applicable in this
Situation, what if there a odd number in the base like 7 🤔

[groomingocean]

I did it like this:

Log(x+1) / log(2) = log(3(x+1)) / log(4)
Log(x+1) / log(2) = log(3(x+1)) / 2log(2)

Then cancel log(2) on both sides

Log(x+1) = log(3(x+1)) / 2
2log(x+1) = log(3(x+1))
2log(x+1) = log(3) + log(x+1)
Log(x+1) = log(3)

So x+1 must be 3

X+1 = 3
X = 2

[dannyjbaylan]

Didn't know this, thank you for the lesson!

[williamraleigh]

How did you get X^2 from (X+1)^2? I thought you couldn't distribute an exponent inside parantheses?

[_karan_x_]

Damn 🙄 i already knew all this at class 8.... actually most of my friends

[valangeloomandac]

but what about if the base is 3 and the other base is 4?

[pambsura]

Why was the squaring not applied to RHS, im not trained in Logarithms. Happy to take notes 👍

[Jack-hdov]

An interesting feature of this problem is that you end up with (x + 1)^2 = 3x + 3 which you can just factor by (x + 1) and get x + 1 = 3 => x = 2.

[CosmoFella]

I didn't yet get to study log, so I'm a bit confused why can you square only one sude of the equasion? Is it a special rule for log or something else?

[lalitasharma]

How can you only square only LHS is this even allowed??

[MrMrkBo]

No way....I didn't know that one either 😅

[Marvellousshorts]

Would you get the same answer if you square root 4, making it log2 and cancelling both side