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

The answer to log_{6}(x+2)-log_{6}(x)=2 is x= 2/35

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

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

x = \frac{2}{35}

Decimal Notation

x = 0.05714 \dots

Solution steps

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

Add

lo g_{6} (x)

to both sides

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

Simplify

lo g_{6} (x + 2) = 2 + lo g_{6} (x)

Apply log rules

x + 2 = 36 x

Solve

x + 2 = 36 x : x = \frac{2}{35}

x = \frac{2}{35}

Verify Solutions:

x = \frac{2}{35}

True

The solution is

x = \frac{2}{35}

ln (x + 1) = ln (x) ln (1)

lo g_{25} (x) = \frac{3}{2}

ln (x + 63) - ln (4 - 3 x) = 6 ln (2)

ln (8) - ln (5 x - 10) = 1

ln (x + 1) - ln (x - 2) = ln (x)

What is the answer to log_{6}(x+2)-log_{6}(x)=2 ?
The answer to log_{6}(x+2)-log_{6}(x)=2 is x= 2/35
Solve for x: log_{6}(x+2)-log_{6}(x)=2
The solution is x= 2/35