Exponential Equation Worksheet With Answers Page 7
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2
3
4
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6
751) log
(x+6) + log
(3x) = 4 (use the plus to multiply rule to rewrite left side with one log)
3
3
Log
(x+6)(3x) = 4
3
2
Log
(3x
+ 18x) = 4
3
4
2
3
= 3x
+ 18x
2
81 = 3x
+ 18x (divide every term by 3 to make numbers smaller)
2
27 = x
+ 6x
2
0 = x
+ 6x – 27
0 = (x+9)(x-3)
x + 9 = 0
x – 3 = 0
x = -9
x = 3
Check x = -9
Log
(-9+6) + log
(3*-9) = 4
3
3
Each of the logs gives an i, this solution doesn’t check. -9 is not a solution
Check x = 3
Log
(3+6) + log
(3*3) = 4
3
3
2 + 2 = 4, this solution check and x = 3 is the only solution to this problem.
Answer: x = 3
(no need to mention the x =-9 as it doesn’t check
It would be okay to write: Answer: x = 3, x = -9 is extraneous)
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