How am i able to solve this?

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

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step-by-step explanation: