Answer:
x=7
Step-by-step explanation:
log2(x+1)−log2(x−5)=2
Use the quotient property of logarithms, logb(x)−logb(y)=logb(xy)
.
log2(x+1x−5)=2
Rewrite log2(x+1x−5)=2
in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then logb(x)=y is equivalent to by=x
.
22=x+1x−5
Cross multiply to remove the fraction.
x+1=22(x−5)
Simplify 22(x−5)
x+1=4x−20
Move all terms containing x
to the left side of the equation.
−3x+1=−20
Move all terms not containing x
to the right side of the equation.
−3x=−21
Divide each term by −3
and simplify.
x=7
