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

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

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

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

x = 8

Solution steps

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

Apply log rules

x^{2} = 16 (x - 4)

Solve

x^{2} = 16 (x - 4) : x = 8

x = 8

Verify Solutions:

x = 8

True

The solution is

x = 8

y, ln (y) = 3 t + 1

2 lo g_{10} (x) = 3 + lo g_{10} (\frac{x}{10})

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

lo g_{5} (x + 30) = 3

lo g_{5} (\frac{( 2 + x )}{10}) = lo g_{5} (\frac{2}{( x + 1 )})

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