What is the answer to log_{4}(x)-log_{4}(x+9)=-1 ?

The answer to log_{4}(x)-log_{4}(x+9)=-1 is x=3

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log_{4}(x)-log_{4}(x+9)=-1

lo g_{4} (x) - lo g_{4} (x + 9) = - 1

x = 3

Solution steps

lo g_{4} (x) - lo g_{4} (x + 9) = - 1

Add

lo g_{4} (x + 9)

to both sides

lo g_{4} (x) - lo g_{4} (x + 9) + lo g_{4} (x + 9) = - 1 + lo g_{4} (x + 9)

Simplify

lo g_{4} (x) = - 1 + lo g_{4} (x + 9)

Apply log rules

x \cdot 4 = x + 9

Solve

x \cdot 4 = x + 9 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

ln (n^{2} + 12) = ln (- 9 n - 2)

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

7.5 = 10.5 + lo g_{10} (x)

lo g_{3} ((r + 10)^{2}) = 4

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

What is the answer to log_{4}(x)-log_{4}(x+9)=-1 ?
The answer to log_{4}(x)-log_{4}(x+9)=-1 is x=3
Solve for x: log_{4}(x)-log_{4}(x+9)=-1
The solution is x=3