What is the answer to log_{2}(3x-2)-log_{2}(x-5)=4 ?

The answer to log_{2}(3x-2)-log_{2}(x-5)=4 is x=6

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log_{2}(3x-2)-log_{2}(x-5)=4

lo g_{2} (3 x - 2) - lo g_{2} (x - 5) = 4

x = 6

Solution steps

lo g_{2} (3 x - 2) - lo g_{2} (x - 5) = 4

Add

lo g_{2} (x - 5)

to both sides

lo g_{2} (3 x - 2) - lo g_{2} (x - 5) + lo g_{2} (x - 5) = 4 + lo g_{2} (x - 5)

Simplify

lo g_{2} (3 x - 2) = 4 + lo g_{2} (x - 5)

Apply log rules

3 x - 2 = 16 (x - 5)

Solve

3 x - 2 = 16 (x - 5) : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

lo g_{9} (x) = 3

0.83 = lo g_{10} (x)

lo g_{2} (x) = 10

lo g_{8} (x + 6) = 1 - lo g_{8} (x + 4)

lo g_{3} (4 x - 1) = 3

What is the answer to log_{2}(3x-2)-log_{2}(x-5)=4 ?
The answer to log_{2}(3x-2)-log_{2}(x-5)=4 is x=6
Solve for x: log_{2}(3x-2)-log_{2}(x-5)=4
The solution is x=6