SOLUTION: Solve the logarithmic equation showing step by step. log2(x^2-11)-log2(2x+5)=1
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Question 1005505: Solve the logarithmic equation showing step by step. log2(x^2-11)-log2(2x+5)=1
Found 2 solutions by MathLover1, Timnewman:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
......change the base to base
.........if log same, then
....solve for
......factor completely
solutions:
=> this is a solution only if assuming a complex-valued logarithm
Answer by Timnewman(323) (Show Source): You can put this solution on YOUR website!
Hi dear,
Follow the step below.
log2(x²-11)-log2(2x+5)=1
Then,
apply law of logarith.
log2[(x²-11)/(2x+5)]=1
but
log2[(x²-11)/(2x+5)=log2 base 2
cancel log from bothside,
(x²-11)/(2x+5)=2
Then,simplify out,
x²-11=2(2x+5)
x²-11=4x+10
x²-4x-21=0
factorize,
(x²-7x)+(3x-21)=0
x(x-7)+3(x-7)=0
(x+3)(x-7)=0
x+3=0 or x-7=0
x=-3 or x=7
Therefore the value of x is -3 or 7.
HOPE THIS HELPS?
::TIMNEWMAN::
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