What is the answer to log_{10}(8x)-log_{10}(1+sqrt(x))=2 ?

The answer to log_{10}(8x)-log_{10}(1+sqrt(x))=2 is x=(11600+sqrt(132000000))/(128)

Solve for x: log_{10}(8x)-log_{10}(1+sqrt(x))=2

The solution is x=(11600+sqrt(132000000))/(128)

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lo g_{10} (8 x) - lo g_{10} (1 + x) = 2

x = \frac{11600 + 132000000}{128}

Decimal

x = 180.38379 \dots

Solution steps

lo g_{10} (8 x) - lo g_{10} (1 + x) = 2

Add

lo g_{10} (1 + x)

to both sides

lo g_{10} (8 x) - lo g_{10} (1 + x) + lo g_{10} (1 + x) = 2 + lo g_{10} (1 + x)

Simplify

lo g_{10} (8 x) = 2 + lo g_{10} (1 + x)

Apply log rules

8 x = 100 (1 + x)

Solve

8 x = 100 (1 + x) : x = \frac{11600 + 132000000}{128}

x = \frac{11600 + 132000000}{128}

Verify Solutions:

x = \frac{11600 + 132000000}{128}

True

The solution is

x = \frac{11600 + 132000000}{128}

x, y = ln (2 x^{2} - 3 y^{2})

lo g_{2 x} (3 x^{2} + 9 x - 20) = 2

4 = lo g_{x} (625)

7 x^{6} ln (x) + x^{6} = 0

lo g_{3} (6 - x) = 3

What is the answer to log_{10}(8x)-log_{10}(1+sqrt(x))=2 ?
The answer to log_{10}(8x)-log_{10}(1+sqrt(x))=2 is x=(11600+sqrt(132000000))/(128)
Solve for x: log_{10}(8x)-log_{10}(1+sqrt(x))=2
The solution is x=(11600+sqrt(132000000))/(128)