Answer:
Option 2nd is correct
x =2
Step-by-step explanation:
Using logarithmic rules:
if [tex]\log_a b = x[/tex], then [tex]a^x = b[/tex]
Given the equation:
[tex]\log_{4x-6} 16 = 4[/tex]
Apply the rules we have;
[tex]16 = (4x-6)^4[/tex]
We can write 16 as:
[tex]16 = 2 \cdot 2 \cdot 2 \cdot 2 = 2^4[/tex]
then;
[tex]2^4 = (4x-6)^4[/tex]
On comparing both sides we have;
[tex]2 = 4x-6[/tex]
Add 6 to both sides we have;
[tex]8 = 4x[/tex]
Divide by 4 to both sides we have;
2 = x
or
x = 2
Therefore, the value of x is, 2
