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

The answer to log_{10}(x+1)-log_{10}(x)=3 is x= 1/999

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

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

x = \frac{1}{999}

Decimal

x = 0.00100 \dots

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 1000 x

Solve

x + 1 = 1000 x : x = \frac{1}{999}

x = \frac{1}{999}

Verify Solutions:

x = \frac{1}{999}

True

The solution is

x = \frac{1}{999}

lo g_{e} (x) = x

ln (x - 5) = 0

lo g_{e} (x) = 4

lo g_{10} (x + 14) = lo g_{10} (x) + lo g_{10} (14)

lo g_{10} (8 x) - lo g_{10} (2) = lo g_{10} (16)

What is the answer to log_{10}(x+1)-log_{10}(x)=3 ?
The answer to log_{10}(x+1)-log_{10}(x)=3 is x= 1/999
Solve for x: log_{10}(x+1)-log_{10}(x)=3
The solution is x= 1/999