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

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eligia | Student, College Freshman | (Level 1) Honors

Posted March 31, 2010 at 1:36 AM via web

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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted March 31, 2010 at 1:46 AM (Answer #1)

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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.

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isbeatbox | Student, Grade 11 | (Level 2) eNoter

Posted March 31, 2010 at 2:05 AM (Answer #2)

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3x-24=2

3x=26

x=8.66....   or x=8+2/3

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

26-24=2

2=2

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tonys538 | Student, Undergraduate | TA | (Level 1) Valedictorian

Posted December 31, 2014 at 5:04 PM (Answer #3)

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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

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