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# log help watch

1. i don't understand why some log equations substitute y into the equations

for example,

log5(x) + 6 logx (5) = 5
log5(x) + 6/log5(x) = 5
let y = log5(x)
so y + 6/y = 5....

or

3^(2x+1) + 5 = 16(3^x)
let y = 3^x
so 3y^2 + 5 = 16y ...

why are we allowed to do that in some cases? how do i know when i should use that technique? i hope my question is clear enough, thanks in advance
2. (Original post by sadboynerd)
i don't understand why some log equations substitute y into the equations

for example,

log5(x) + 6 logx (5) = 5
log5(x) + 6/log5(x) = 5
let y = log5(x)
so y + 6/y = 5....

or

3^(2x+1) + 5 = 16(3^x)
let y = 3^x
so 3y^2 + 5 = 16y ...

why are we allowed to do that in some cases? how do i know when i should use that technique? i hope my question is clear enough, thanks in advance
It's just a technique you can use to help you solve these kinds of equations. You can use it any time you like if it's useful.

E.g. if you had then using won't be much help because you'll be left with

But if you have something like then this can be written as

Then if you use you get

This is a quadratic which you should find easier to deal with than the equation above it. You just have to remember to substitute back in at the end.

Does this make sense?
3. (Original post by notnek)
It's just a technique you can use to help you solve these kinds of equations. You can use it any time you like if it's useful.

E.g. if you had then using won't be much help because you'll be left with

But if you have something like then this can be written as

Then if you use you get

This is a quadratic which you should find easier to deal with than the equation above it. You just have to remember to substitute back in at the end.

Does this make sense?
it does make sense but what would be an alternative way to solving it without turning it into a quadratic?
4. (Original post by sadboynerd)
it does make sense but what would be an alternative way to solving it without turning it into a quadratic?

This equation is a quadratic since you have something of the form

So the only way to solve it is by using quadratic equations methods.

But you don't have to use a substitution if you don't want to. You could just see that it is a quadratic and attempt to factorise:

What I've done here is factorise just like if there was a single variable instead of e.g.

So you can set each bracket to 0 and solve. But most people find substitution makes this process easier.
5. thank you lots for taking the time to explain!!!

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