SOLUTION: Solve the logarithmic equation showing step by step. log2(x^2-11)-log2(2x+5)=1

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Solve the logarithmic equation showing step by step. log2(x^2-11)-log2(2x+5)=1      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

log%282%2C%28x%5E2-11%29%29-log%282%2C%282x%2B5%29%29=1

log%282%2C%28x%5E2-11%29%2F%282x%2B5%29%29=1......change the base to base 10

log%28%28x%5E2-11%29%2F%282x%2B5%29%29%2Flog%28%282%29%29=1

log%28%28x%5E2-11%29%2F%282x%2B5%29%29=1%2Alog%28%282%29%29

log%28%28x%5E2-11%29%2F%282x%2B5%29%29=log%28%282%29%29.........if log same, then

%28x%5E2-11%29%2F%282x%2B5%29=2....solve for x

x%5E2-11=2%282x%2B5%29

x%5E2-11=4x%2B10

x%5E2-11-4x-10=0

x%5E2-4x-21=0......factor completely

x%5E2-7x%2B3x-21=0

%28x%5E2-7x%29%2B%283x-21%29=0

x%28x-7%29%2B3%28x-7%29=0

%28x-7%29%28x%2B3%29+=+0

solutions:
x=7
x=-3=> this is a solution only if assuming a complex-valued logarithm


Answer by Timnewman(323) About Me  (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::