What is the answer to log_{3}(2x-1)-log_{3}(x-4)=2 ?

The answer to log_{3}(2x-1)-log_{3}(x-4)=2 is x=5

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log_{3}(2x-1)-log_{3}(x-4)=2

lo g_{3} (2 x - 1) - lo g_{3} (x - 4) = 2

x = 5

Solution steps

lo g_{3} (2 x - 1) - lo g_{3} (x - 4) = 2

Add

lo g_{3} (x - 4)

to both sides

lo g_{3} (2 x - 1) - lo g_{3} (x - 4) + lo g_{3} (x - 4) = 2 + lo g_{3} (x - 4)

Simplify

lo g_{3} (2 x - 1) = 2 + lo g_{3} (x - 4)

Apply log rules

2 x - 1 = 9 (x - 4)

Solve

2 x - 1 = 9 (x - 4) : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

0.456 = ln (x^{2})

x, ln (y) = - ln (x) + c

0.6 = lo g_{10} (x)

lo g_{10} (x^{2}) = 2

ln (27) - ln (x) = ln (x - 6)

What is the answer to log_{3}(2x-1)-log_{3}(x-4)=2 ?
The answer to log_{3}(2x-1)-log_{3}(x-4)=2 is x=5
Solve for x: log_{3}(2x-1)-log_{3}(x-4)=2
The solution is x=5