What is the answer to log_{4}(4x)-log_{4}(x-6)=2 ?

The answer to log_{4}(4x)-log_{4}(x-6)=2 is x=8

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log_{4}(4x)-log_{4}(x-6)=2

lo g_{4} (4 x) - lo g_{4} (x - 6) = 2

x = 8

Solution steps

lo g_{4} (4 x) - lo g_{4} (x - 6) = 2

Add

lo g_{4} (x - 6)

to both sides

lo g_{4} (4 x) - lo g_{4} (x - 6) + lo g_{4} (x - 6) = 2 + lo g_{4} (x - 6)

Simplify

lo g_{4} (4 x) = 2 + lo g_{4} (x - 6)

Apply log rules

4 x = 16 (x - 6)

Solve

4 x = 16 (x - 6) : x = 8

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

ln (x) = - 4.3178

x = ln (3.2 x 1 0^{4})

lo g_{2} (x) - 8 lo g_{10} (x) + 15 = 0

ln ∣ x ∣ - x = 0

ln (2 b) = ln (4 b)

What is the answer to log_{4}(4x)-log_{4}(x-6)=2 ?
The answer to log_{4}(4x)-log_{4}(x-6)=2 is x=8
Solve for x: log_{4}(4x)-log_{4}(x-6)=2
The solution is x=8