Solve the equation log 3(x-8)=2.
Before solving the equation, which is a logarithmical equation, we have to find out the restrictive domain for the x values.
For this reason, we have to impose the condition that x-8>0.
x>8, that means that x belongs to the interval (8, +inf).
Now, we can solve the equation:
The solution is acceptable because is belonging to the interval of allowed x values.
The equation `log_3(x-8)=2` has to be solved for x.
If the logarithm of a number y to base b is x, `log_b y = x` , then y is equal to b^x.
Using this relation, for `log_3(x - 8) = 2` , the base of the logarithm is 3
This gives x - 8 = 3^2
x - 8 = 9
x = 9+8
x = 17
The solution of the equation is x = 17
x=8.66.... or x=8+2/3