SOLUTION: Need help solving equations such as:
log 11 (3x+10)= log 11 (x+6)
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Question 616022: Need help solving equations such as:
log 11 (3x+10)= log 11 (x+6)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
The next step in a problem like is is based on some simple logic. Base 11 logs represent exponents for 11. In this case the left side is the exponent for 11 that results in 3x+10 while the right side is the exponent for 11 that results in x+6. The equation says that these exponents are equal. So if the exponents are equal then the results of raising 11 to those equal powers must be equal. So:
3x+10 = x+6
After all, we can't have some power of 11 resulting in two different/unequal numbers. The equation is now a very easy equation to solve. Subtracting x from each side we get:
2x+10 = 6
Subtracting 10:
2x = -4
Dividing by 2:
x = -2
Checking solutions to equations where the variable is in the argument of a log is not optional. You must at least ensure that your "solution" makes the arguments positive. (If a "solution" makes an argument zero or negative you must reject it.) Use the original equation to check:
Checking x = -2:
Check!
So x = -2 is the solution to your equation.
Note: It is the argument of a logarithm that cannot be negative (or zero). It is OK, as in this equation, for the variable to be zero or negative.
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