What is the answer to log_{2}(x+5)-log_{2}(x-5)=3 ?

The answer to log_{2}(x+5)-log_{2}(x-5)=3 is x= 45/7

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log_{2}(x+5)-log_{2}(x-5)=3

lo g_{2} (x + 5) - lo g_{2} (x - 5) = 3

x = \frac{45}{7}

Solution steps

lo g_{2} (x + 5) - lo g_{2} (x - 5) = 3

Add

lo g_{2} (x - 5)

to both sides

lo g_{2} (x + 5) - lo g_{2} (x - 5) + lo g_{2} (x - 5) = 3 + lo g_{2} (x - 5)

Simplify

lo g_{2} (x + 5) = 3 + lo g_{2} (x - 5)

Apply log rules

x + 5 = 8 (x - 5)

Solve

x + 5 = 8 (x - 5) : x = \frac{45}{7}

x = \frac{45}{7}

Verify Solutions:

x = \frac{45}{7}

True

The solution is

x = \frac{45}{7}

lo g_{4} (5 x - 4) = 2 x

lo g_{12} (4 x + 2) = 0

ln (\frac{( x + 3 )}{( x - 1 )}) = 1

lo g_{x} (4) = lo g_{10} (100)

lo g_{5} (x + 5) + lo g_{5} (x - 4) = 3

What is the answer to log_{2}(x+5)-log_{2}(x-5)=3 ?
The answer to log_{2}(x+5)-log_{2}(x-5)=3 is x= 45/7
Solve for x: log_{2}(x+5)-log_{2}(x-5)=3
The solution is x= 45/7