Logarithm problem

[trail raft]

hey i need help for this problem

[primal sun]

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[spice oriole]

,rotate

[spice oriole]

So I assume it’s solve the SOE

For top equation, use the fact that ln(a)^b = b • ln(a) and vice versa

So ln(y) = -4 • ln(x+1) or 1/ln(x+1)^4

[trail raft]

like this

Am still blocked

[trail raft]

sorry but what does it means

[upbeat tusk]

Well, no. ln(a^b) = b ln(a). ln(a)^b does not.

[calm pilot]

Ln(a)^b can mean ln(a^b) not specifically ln^b(a)

[trail raft]

no it means here

ln[(x+1)^4]

so 4ln(x+1)

But i Can't find the solution i tried to simplify it by assuming lny= 4lnx+1

it gives anything

[upbeat tusk]

...missed a negative.

[thorn zenith]

If you we assume here ln(a^b)= bln(a) you can express x in term of y on the second line

Using the properties of ln

Then you can substitute on the first line and solve for one of the variables

[trail raft]

Yeah its missed it when i wrote it on discord put i puuted it in my calculus

[upbeat tusk]

You also missed parentheses.

[trail raft]

heres de problem when a substitute one the other line to solve it i dk how to do it i get this (the picture is comming)

[trail raft]

yeah..

look

[thorn zenith]

WoW that looks annoying

[thorn zenith]

Well you could write x=x+1-1

Then develop ((x+1)-1)(x+1)^4=(x+1)^5-(x+1)^4

Let X=x+1

Then you need to solve X^5-X^4=1

Find the roots of X^5-X^4-1

Not all of the roots because note that logarithms are involved so you need x>0 and x+1>1 thus X>1

Also this polynomial doesn’t have any rational roots

[thorn zenith]

There is only 1 solution on the interval ]1,2]