Logarithmic equations

[rapid vapor]

Can someone please help me with the logarithm question, I've been trying for hours 😭

[sacred rose]

Maybe I try

[rapid vapor]

Thanks

[sacred rose]

I think it's best to simplify the 2nd equation

[rapid vapor]

To something like log(xy) = log6

Xy = 6

[sacred rose]

yes

[rapid vapor]

But I got lost after simplifying both

[sacred rose]

Let's consider the above

[vestal spire]

𝔸dωn𝓲²s

[sacred rose]

See what I did?

[rapid vapor]

Yeh

I did that already

[sacred rose]

Now we can make use of another one

another log property

[rapid vapor]

In eqn 2

[sacred rose]

no 1

we can use

log(a) + log(b) = log(ab)

right?

[rapid vapor]

Mistake

[sacred rose]

huh where

[rapid vapor]

Yeh

[sacred rose]

ok

[rapid vapor]

No worries

[rapid vapor]

So log (y^2(x-1)) = log 3^2

[sacred rose]

yes

[quiet mural]

you can solve for x in terms of y pretty easily with the second equation

[vestal spire]

𝔸dωn𝓲²s

[sacred rose]

Notice how we can substitute xy from the second equation

and then solve for y

in the first one

[rapid vapor]

Yeh

[sacred rose]

When you figured y

you can figure x

[rapid vapor]

Ok let me try solving it again

[quiet mural]

you can compare, i got y = 15/4

erm nvm i did that wrong

[sacred rose]

I think y = 3

[quiet mural]

i got sqrt10

for y

[sacred rose]

hmm

[quiet mural]

i could've done it wrong haha

[rapid vapor]

Just to check when I substitute xy it's log( 6 * y - y^2 ) = log 3

[sacred rose]

yes

it seems to work out nicely that way

[rapid vapor]

So the logs cancel out

[sacred rose]

basically

[rapid vapor]

But what I'm getting is decimal for y

[sacred rose]

ok

are you also getting sqrt(10)?

like the guy above

,w -y^2+6y-3^2 = 0

[vestal spire]

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𝔸dωn𝓲²s

[sacred rose]

you forgot the square

it's 3^2

[rapid vapor]

I just it now

So if y = 3
And I put it into log x + log y = log 6

[sacred rose]

yes

put it into

log(xy) = log(6)

then you get

log(3x) = log(6)

what has x to be

[rapid vapor]

2

[sacred rose]

exactly

you sat for hours

[rapid vapor]

I've been on this question all day 😔

It been bothering me

Thank you @sacred rose

[sacred rose]

thank you too

[rapid vapor]

For what

[short solstice]

If you are done with this channel, please mark your problem as solved by typing .close

[rapid vapor]

.close