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

The answer to log_{4}(x-2)-log_{4}(x-5)=2 is x= 26/5

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

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

x = \frac{26}{5}

Decimal Notation

x = 5.2

Solution steps

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

Add

lo g_{4} (x - 5)

to both sides

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

Simplify

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

Apply log rules

x - 2 = 16 (x - 5)

Solve

x - 2 = 16 (x - 5) : x = \frac{26}{5}

x = \frac{26}{5}

Verify Solutions:

x = \frac{26}{5}

True

The solution is

x = \frac{26}{5}

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What is the answer to log_{4}(x-2)-log_{4}(x-5)=2 ?
The answer to log_{4}(x-2)-log_{4}(x-5)=2 is x= 26/5
Solve for x: log_{4}(x-2)-log_{4}(x-5)=2
The solution is x= 26/5