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

The answer to log_{2}(3x+5)-log_{2}(x-5)=3 is x=9

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

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

x = 9

Solution steps

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

Add

lo g_{2} (x - 5)

to both sides

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

Simplify

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

Apply log rules

3 x + 5 = 8 (x - 5)

Solve

3 x + 5 = 8 (x - 5) : x = 9

x = 9

Verify Solutions:

x = 9

True

The solution is

x = 9

lo g_{3} (10) - lo g_{3} (- 2 x) = 4

lo g_{3} (8 x - 2) + lo g_{3} (x - 1) = 2

lo g_{5} (X) = - 2

ln (3 x + e) = 3

ln (x^{7}) - ln (x^{4}) = 3

What is the answer to log_{2}(3x+5)-log_{2}(x-5)=3 ?
The answer to log_{2}(3x+5)-log_{2}(x-5)=3 is x=9
Solve for x: log_{2}(3x+5)-log_{2}(x-5)=3
The solution is x=9