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tdahna0403
28.09.2019 •
Mathematics
Which is the only solution to the equation log3(x2 + 6x) = log3(2x + 12)?
x = –6
x = –2
x = 0
x = 2
x = 6
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Ответ:
the answer is option 4: x=2
Ответ:
Option 4th is correct
x = 2
Step-by-step explanation:
Using logarithmic rule:
then; x = y
Given the equation:
Apply the rule:
Subtract 2x from both sides we have;
Subtract 12 from both sides we have;
⇒![x^2+6x-2x-12 = 0](/tpl/images/0270/6675/5d2e3.png)
⇒![x(x+6)-2(x+6)= 0](/tpl/images/0270/6675/40159.png)
⇒![(x+6)(x-2)= 0](/tpl/images/0270/6675/d7f79.png)
by zero product property we have:
x+6 =0 and x-2 = 0
⇒x= -6 and x = 2
Since, at x = -6 it does not satisfy the given equation.
Therefore, the only solution to the given equation is, x = 2
Ответ: