What is the answer to log_{3}(10-x)-log_{3}(x+2)=1 ?

The answer to log_{3}(10-x)-log_{3}(x+2)=1 is x=1

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log_{3}(10-x)-log_{3}(x+2)=1

lo g_{3} (10 - x) - lo g_{3} (x + 2) = 1

x = 1

Solution steps

lo g_{3} (10 - x) - lo g_{3} (x + 2) = 1

Add

lo g_{3} (x + 2)

to both sides

lo g_{3} (10 - x) - lo g_{3} (x + 2) + lo g_{3} (x + 2) = 1 + lo g_{3} (x + 2)

Simplify

lo g_{3} (10 - x) = 1 + lo g_{3} (x + 2)

Apply log rules

10 - x = 3 (x + 2)

Solve

10 - x = 3 (x + 2) : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

lo g_{10} (y^{10}) = 2

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

2 lo g_{2} (x) = 4

(ln (x))^{2} = 10 - 9 ln (x)

ln (x + 9) + ln (x - 5) = 2 ln (x)

What is the answer to log_{3}(10-x)-log_{3}(x+2)=1 ?
The answer to log_{3}(10-x)-log_{3}(x+2)=1 is x=1
Solve for x: log_{3}(10-x)-log_{3}(x+2)=1
The solution is x=1