Answer:
[tex]x=3.1950[/tex]
Step-by-step explanation:
Given:
The equation to solve is given as:
[tex]\log_8 12=x-2[/tex]
In order to solve this, we use the base change formula of logarithms.
The base change formula is given as:
[tex]\log_a b=\frac{\log b}{\log a}[/tex]
Therefore, the equation can be rewritten as:
[tex]\frac{\log 12}{\log 8}=x-2[/tex]
Adding 2 on both the sides, we get:
[tex]x=2+\frac{\log 12}{\log 8}[/tex]
Now, we know that, [tex]\log 12=1.07918\ and\ \log 8=0.9031[/tex]
Plug in these values and solve for 'x'. This gives,
[tex]x=2+\frac{1.07918}{0.9031}\\\\x=2+1.19497=3.19497\approx3.1950[/tex]
Therefore, the value of 'x' is 3.1950 rounded to four decimal places.
