# Solve the equation log 3(x-8)=2.

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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:

x-8=3^2

x-8=9

x=9+8

**x=17**

The solution is acceptable because is belonging to the interval of allowed x values.

3x-24=2

3x=26

x=8.66.... or x=8+2/3

3((8+2/3)-8)=2

26-24=2

2=2

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