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

The answer to log_{10}(x+2)-log_{10}(x)=3 is x= 2/999

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

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

x = \frac{2}{999}

Decimal Notation

x = 0.00200 \dots

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

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

Apply log rules

x + 2 = 1000 x

Solve

x + 2 = 1000 x : x = \frac{2}{999}

x = \frac{2}{999}

Verify Solutions:

x = \frac{2}{999}

True

The solution is

x = \frac{2}{999}

lo g_{5} (x - 11) + lo g_{5} (x - 6) = 2

6 = - lo g_{x} (x)

lo g_{10} (m) = 8.92

lo g_{10} (x) = - 0.25

lo g_{10} (x) = - 0.12

What is the answer to log_{10}(x+2)-log_{10}(x)=3 ?
The answer to log_{10}(x+2)-log_{10}(x)=3 is x= 2/999
Solve for x: log_{10}(x+2)-log_{10}(x)=3
The solution is x= 2/999