Exponential Equation Worksheet With Answers Page 6
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747) log
(x+6) – log
(3x+2)=-1 (use minus to divide rule to rewrite left side with one log)
2
2
��+6
������
= −1
2
3��+2
��+6
−1
2
=
-1
1
(write 2
as ½
)
3��+2
1
��+6
=
(cross multiply)
2
3��+2
3x + 2 = 2x + 12
Answer: x = 10
49) log
x + log
(x+6) = 3 (use the plus to multiply rule to rewrite left side with one log)
3
3
Log
(x)(x+6) = 3
3
2
Log
(x
+ 6x) = 3 (write in exponential form)
3
3
2
3
= x
+ 6x
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) + log
(-9+6) =3
3
3
I get i on the left side, so this doesn’t check and -9 is not a solution
Check x = 3
Log
3 + log
(3+6) = 3
3
3
1 + 2 = 3 (3 is a solution)
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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