Question

If log (log (6 + log5(x + 1))) = 0, then find the value of x.
O 125
O 624
O 625
O 216​

Answer 1

Step-by-step explanation:

Annexure contains the solution

Answer 2

Given:

$log (log (6 + log5(x + 1))) = 0$

To Find:

The value of x

Solution:

Here we will use some rules and special cases of logarithm like

$log(1)=0\\log(10)=1$

⇒$log (log (6 + log5(x + 1))) = 0$

⇒$log(6+log_{5} (x+1)=1$

⇒$6 + log_{5} (x + 1) = 10$

⇒$log_{5} (x + 1) = 4$

Now,

   $log_{a} b=c\\a^{c} =b$

⇒ $log_{5} (x + 1) = 4$

⇒ $x+1=5^{4}$

⇒ $x=625-1$

⇒ $x=624$

Hence, the value of x is 624