Answer:
[tex]\boxed{\sf x = 7 }[/tex]
Step-by-step explanation:
We are here given a logarithmic equation and we need to solve it out and then find the value of x. The given equation is ,
[tex]\sf\longrightarrow log_6 + log_6 ( x -1) = 1 [/tex]
Here I am assuming that the base of the logarithm is 6 . The equation can be written as ,
[tex]\sf\longrightarrow log_6 1+ log_6 ( x -1) = 1 [/tex]
Recall the property of log as , [tex]\sf log_x a + log_x b = log_x(ab) [/tex] , on using this property we have ,
[tex]\sf\longrightarrow log_6 \{ 1 ( x -1)\} = 1 [/tex]
Simplify ,
[tex]\sf\longrightarrow log_6 ( x -1) = 1 [/tex]
We know that , if [tex]\sf log_a b = c [/tex] then in expotential form it can be expressed as [tex]\sf a^c = b [/tex] . Using this we have ,
[tex]\sf\longrightarrow 6^1 = x - 1[/tex]
Simplify ,
[tex]\sf\longrightarrow 6 = x - 1[/tex]
Add 1 both sides ,
[tex]\sf\longrightarrow x = 6 + 1[/tex]
Therefore ,
[tex]\sf\longrightarrow \boxed{\blue{\sf \quad x = 7\quad }} [/tex]
Hence the value of x is 7 .
