Question

1+2log(x+2)5=log 5(x+2)

Answer 1

I hope this answer would be helpful for you

Answer 2

Answer:

The value of x is 23,-1,8.

Step-by-step explanation:

Given : $1+2\log_{(x+2)}5=\log_5(x+2)$

To find : The value of x?

Solution :

$1+2\log_{(x+2)}5=\log_5(x+2)$

$1+\frac{2}{\log_5(x+2)}=\log_5(x+2)$

$\log_5(x+2)+2=(\log_5(x+2))^2$

Let  $\log_5(x+2)=t$

Now, the equation became

$t+2=t^2$

$t^2-t-2=0$

$(t+1)(t-2)$

$t=-1, t=2$

Substitute back we get,

$\log_5(x+2)=t$

When t=-1

$\log_5(x+2)=-1$

$x+2=\frac{1}{5}$

$x=-1,8$

When t=2

$\log_5(x+2)=2$

$x+2=25$

$x=23$

Therefore, The value of x is 23,-1,8.