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

The answer to log_{10}(x+1)-log_{10}(x)=1 is x= 1/9

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

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

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 10 x

Solve

x + 1 = 10 x : x = \frac{1}{9}

x = \frac{1}{9}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

lo g_{3} (x) - 2 \cdot lo g_{13} (x) = 6

(lo g_{10} (x))^{3} = 0

lo g_{10} (\frac{( x + 4 )}{( x - 2 )}) = 2

lo g_{2} (x^{2} - 3 x) = 4

lo g_{5} (lo g_{4} (x)) = 0

What is the answer to log_{10}(x+1)-log_{10}(x)=1 ?
The answer to log_{10}(x+1)-log_{10}(x)=1 is x= 1/9
Solve for x: log_{10}(x+1)-log_{10}(x)=1
The solution is x= 1/9