What is the answer to log_{6}(x+3)-log_{6}(x-2)=1 ?

The answer to log_{6}(x+3)-log_{6}(x-2)=1 is x=3

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log_{6}(x+3)-log_{6}(x-2)=1

lo g_{6} (x + 3) - lo g_{6} (x - 2) = 1

x = 3

Solution steps

lo g_{6} (x + 3) - lo g_{6} (x - 2) = 1

Add

lo g_{6} (x - 2)

to both sides

lo g_{6} (x + 3) - lo g_{6} (x - 2) + lo g_{6} (x - 2) = 1 + lo g_{6} (x - 2)

Simplify

lo g_{6} (x + 3) = 1 + lo g_{6} (x - 2)

Apply log rules

x + 3 = 6 (x - 2)

Solve

x + 3 = 6 (x - 2) : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{10} (x) - lo g_{10} (x + 6) = - 1

lo g_{2} (x) = - 2

ln (3 x - 11) = 6

0.66 = ln (x)

x, - 4 lo g_{2} (5 x) = - 12

What is the answer to log_{6}(x+3)-log_{6}(x-2)=1 ?
The answer to log_{6}(x+3)-log_{6}(x-2)=1 is x=3
Solve for x: log_{6}(x+3)-log_{6}(x-2)=1
The solution is x=3