What is the answer to log_{e}(x+2)-log_{e}(3x)=0 ?

The answer to log_{e}(x+2)-log_{e}(3x)=0 is x=1

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log_{e}(x+2)-log_{e}(3x)=0

lo g_{e} (x + 2) - lo g_{e} (3 x) = 0

x = 1

Solution steps

lo g_{e} (x + 2) - lo g_{e} (3 x) = 0

Add

lo g_{e} (3 x)

to both sides

lo g_{e} (x + 2) - lo g_{e} (3 x) + lo g_{e} (3 x) = 0 + lo g_{e} (3 x)

Simplify

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

Apply log rules

x + 2 = 3 x

Solve

x + 2 = 3 x : x = 1

x = 1

Verify Solutions:

x = 1

True

The solution is

x = 1

lo g_{10} (9 x) + lo g_{10} (3 x) = 3

lo g_{2 x} (81) = \frac{4}{3}

lo g_{10} (x) = - 4.67

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

ln (x + 4) = 1

What is the answer to log_{e}(x+2)-log_{e}(3x)=0 ?
The answer to log_{e}(x+2)-log_{e}(3x)=0 is x=1