What is the answer to log_{10}(x)+log_{10}(x+1)=5 ?

The answer to log_{10}(x)+log_{10}(x+1)=5 is x=(-1+sqrt(400001))/2

Solve for x: log_{10}(x)+log_{10}(x+1)=5

The solution is x=(-1+sqrt(400001))/2

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lo g_{10} (x) + lo g_{10} (x + 1) = 5

x = \frac{- 1 + 400001}{2}

Decimal Notation

x = 315.72816 \dots

Solution steps

lo g_{10} (x) + lo g_{10} (x + 1) = 5

Apply log rules

x (x + 1) = 100000

Solve

x (x + 1) = 100000 : x = \frac{- 1 + 400001}{2}, x = \frac{- 1 - 400001}{2}

x = \frac{- 1 + 400001}{2}, x = \frac{- 1 - 400001}{2}

Verify Solutions:

x = \frac{- 1 + 400001}{2}

True

, x = \frac{- 1 - 400001}{2}

False

The solution is

x = \frac{- 1 + 400001}{2}

lo g_{2} (ln (x)) = 1

lo g_{3} (5 x - 8) = 1

x, ln (x) = 5

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

lo g_{b} (\frac{1}{16}) = - 2

What is the answer to log_{10}(x)+log_{10}(x+1)=5 ?
The answer to log_{10}(x)+log_{10}(x+1)=5 is x=(-1+sqrt(400001))/2
Solve for x: log_{10}(x)+log_{10}(x+1)=5
The solution is x=(-1+sqrt(400001))/2