SOLUTION: Log2(x^2-9)=4

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Question 1138529: Log2(x^2-9)=4
Found 3 solutions by MathLover1, MathTherapy, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
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log%282%2C%28x%5E2-9%29%29=4
log%28%28x%5E2-9%29%29%2Flog%282%29=4
log%28%28x%5E2-9%29%29=4log%282%29
log%28%28x%5E2-9%29%29=log%282%5E4%29
log%28%28x%5E2-9%29%29=log%2816%29........if log same, then
x%5E2-9=16
x%5E2=16%2B9
x%5E2=25
x=sqrt%2825%29
x=5 or x=-5


Answer by MathTherapy(10552) About Me  (Show Source):
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Log2(x^2-9)=4
matrix%281%2C3%2C+log+%282%2C+%28x%5E2+-+9%29%29%2C+%22=%22%2C+4%29

matrix%281%2C3%2C+x%5E2+-+9%2C+%22=%22%2C+2%5E4%29 ------ Converting to EXPONENTIAL form

matrix%281%2C3%2C+x%5E2+-+9+-+16%2C+%22=%22%2C+0%29

matrix%281%2C3%2C+x%5E2+-+25%2C+%22=%22%2C+0%29

(x - 5)(X + 5) = 0

Answer by ikleyn(52803) About Me  (Show Source):
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.
log%282%2C%28x%5E2-9%29%29 = 4


is equivalent to


    x%5E2-9 = 2%5E4    (by the definition of the logarithm)


which, in turn, is equivalent to


    x%5E2 = 16%2B9,   or

    x%5E2 = 25.


Hence,  x = sqrt%2825%29 = +/- 5.


ANSWER.  The given equation has two solutions,  x= 5  and  x= -5.