What is the answer to log_{9}(x+2)-log_{9}(x-6)=1 ?

The answer to log_{9}(x+2)-log_{9}(x-6)=1 is x=7

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log_{9}(x+2)-log_{9}(x-6)=1

lo g_{9} (x + 2) - lo g_{9} (x - 6) = 1

x = 7

Solution steps

lo g_{9} (x + 2) - lo g_{9} (x - 6) = 1

Add

lo g_{9} (x - 6)

to both sides

lo g_{9} (x + 2) - lo g_{9} (x - 6) + lo g_{9} (x - 6) = 1 + lo g_{9} (x - 6)

Simplify

lo g_{9} (x + 2) = 1 + lo g_{9} (x - 6)

Apply log rules

x + 2 = 9 (x - 6)

Solve

x + 2 = 9 (x - 6) : x = 7

x = 7

Verify Solutions:

x = 7

True

The solution is

x = 7

x, ln (x^{2} + y) = 0

lo g_{10} (x) = 0.12

lo g_{12} (4 x - 2) = 0

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

ln (\frac{1}{x}) = 4

What is the answer to log_{9}(x+2)-log_{9}(x-6)=1 ?
The answer to log_{9}(x+2)-log_{9}(x-6)=1 is x=7
Solve for x: log_{9}(x+2)-log_{9}(x-6)=1
The solution is x=7