Question

x-3/x+1 = 3/5 urgently need​

Answer 1

Answer:

$\Huge\sf\blue{Answer}$

4(3x−1)=3(5x)

If f(x)=g(x),then ln(f(x))=ln(g(x))

ln(4(3x−1))=ln(3⋅5x)

Apply log rule: logc(ab)=logc(a)+logc(b)

ln(3⋅5x)=ln(3)+ln(5x)=ln(4(3x−1))=ln(3)+ln(5x)

Apply log rule: loga(xb)=b⋅loga(x)

ln(4(3x−1))=(3x−1)ln(4), ln(5x)=xln(5)so we get (3x−1)ln(4)=ln(3)+xln(5)

To simplify (3x−1)ln(4)

First, simplify ln(4)

Rewrite 4 in power base form: 4=22

=ln(22)

Apply log rule: loga(xb)=b⋅loga(x)

ln(22)=2ln(2)

=2ln(2)

So now, 2ln(2)(3x−1)

So now we have 2ln(2)(3x−1)=ln(3)+xln(5)

To solve, first expand ln(2)(3x−1)

Distribute parenthesis using a(b+c)=ab+ac

a=2ln(2),b=3x,c=−1

=2ln(2)⋅3x+2ln(2)(−1)

Since +(−a)=−a , so we get

=2ln(2)⋅3x−2ln(2)⋅1

or by simplifying =6xln(2)−2ln(2)

So now we have 6xln(2)−2ln(2)=ln(3)+xln(5)

Add 2ln(2) on both sides,

6xln(2)−2ln(2)+2ln(2)=ln(3)+xln(5)+2ln(2)

refining, we get 6xln(2)=ln(3)+xln(5)+2ln(2)

Subtracting xln(5) from both sides

6xln(2)−xln(5)=ln(3)+xln(5)+2ln(2)−xln(5)

and refining, 6xln(2)−xln(5)=ln(3)+2ln(2)

Let us factor 6xln(2)−xln(5) by factoring out the common term x

so we get x(6ln(2)−ln(5))

x(6ln(2)−ln(5))=ln(3)+2ln(2)

Divide both sides by 6ln(2)−ln(5)

x(6ln(2)−ln(5))6ln(2)−ln(5)=ln(3)+2ln(2)6ln(2)−ln(5)

Now we refine ln(3)+2ln(2)6ln(2)−ln(5)

First we simplify 6ln(2)−ln(5) by applying log rule: alogc(b)=logc(ba)

ln(26)−ln(5)=ln(265)

and since 26=64 , so ln(645)

and we get =ln(3)+2ln(2)ln(645)

Next simplify ln(3)+2ln(2) by applying log rule alogc(b)=logc(ba)

So because 2ln(2)=ln(22) , we get

=ln(3)+ln(22)

Apply log rule: logc(a)+logc(b)=logc(ab)

ln(3)+ln(22)=ln(22⋅3)=ln(12)

So now the final solution is x=ln(12)ln(645)

Answer 2

Answer:

9

Step-by-step explanation:

by cross multiplication

5(x-3)=3(x+1)

5x-15=3x+3

5x-3x=3+15

2x=18

x=18/2

x=9