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

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

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

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

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

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

Decimal Notation

x = 316.72816 \dots

Solution steps

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

Apply log rules

100000 = x (x - 1)

Solve

100000 = x (x - 1) : 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}

2 x - e^{2} lo g_{e} (x) = 0

lo g_{5} (x + 2) + lo g_{5} (x - 2) = 1

lo g_{8} (2 n - 3) = lo g_{8} (4 - n)

2 7^{l o g_{9} (x)} = x^{1.5}

lo g_{3^{2}} ((x - 1)^{2}) = - 1

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