Neal D.

asked • 11/02/17

logarithmic equation log2(x+4)+log2(x+7)=2

solve the logarithmic equation log2(x+4)+log2(x+7)=2
 
Please Explain

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Andrew M. answered • 11/02/17

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log2(x+4)+log2(x+7)=2
 
Note:  Logbx + logby = logbxy
 
log2[(x+4)(x+7)] = 2
 
Note:  logba=n   then  bn = a
 
(x+4)(x+7) = 22
x2 + 11x + 28 = 4
x2 + 11x + 24 = 0
(x+3)(x+8) = 0
 
x = -3 or x = -8
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Mark M.

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-8 is extraneous because log2(-8+7)  and log2(-8+4) are both undefined.  So, -3 is the only solution.  
 
Mark M (Bayport, NY)
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11/03/17

Andrew M.

Thank you Mark.  :-)
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11/03/17

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