What is the answer to log_{2}(x+5)-log_{2}(x-1)=5 ?

The answer to log_{2}(x+5)-log_{2}(x-1)=5 is x= 37/31

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log_{2}(x+5)-log_{2}(x-1)=5

lo g_{2} (x + 5) - lo g_{2} (x - 1) = 5

x = \frac{37}{31}

Decimal Notation

x = 1.19354 \dots

Solution steps

lo g_{2} (x + 5) - lo g_{2} (x - 1) = 5

Add

lo g_{2} (x - 1)

to both sides

lo g_{2} (x + 5) - lo g_{2} (x - 1) + lo g_{2} (x - 1) = 5 + lo g_{2} (x - 1)

Simplify

lo g_{2} (x + 5) = 5 + lo g_{2} (x - 1)

Apply log rules

x + 5 = 32 (x - 1)

Solve

x + 5 = 32 (x - 1) : x = \frac{37}{31}

x = \frac{37}{31}

Verify Solutions:

x = \frac{37}{31}

True

The solution is

x = \frac{37}{31}

6 (ln (4 x - 9)) + 14 = 26

3.1 = - lo g_{10} (x)

x, 6.07 = - lo g_{10} (x)

lo g_{5} (- 7 - 5 x) = 2

lo g_{1} (x - 1) = 5

What is the answer to log_{2}(x+5)-log_{2}(x-1)=5 ?
The answer to log_{2}(x+5)-log_{2}(x-1)=5 is x= 37/31
Solve for x: log_{2}(x+5)-log_{2}(x-1)=5
The solution is x= 37/31