What is the answer to log_{10}(4x)-log_{10}(12+sqrt(x))=2 ?

The answer to log_{10}(4x)-log_{10}(12+sqrt(x))=2 is x=(19600+sqrt(292000000))/(32)

Solve for x: log_{10}(4x)-log_{10}(12+sqrt(x))=2

The solution is x=(19600+sqrt(292000000))/(32)

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lo g_{10} (4 x) - lo g_{10} (12 + x) = 2

x = \frac{19600 + 292000000}{32}

Decimal

x = 1146.50023 \dots

Solution steps

lo g_{10} (4 x) - lo g_{10} (12 + x) = 2

Add

lo g_{10} (12 + x)

to both sides

lo g_{10} (4 x) - lo g_{10} (12 + x) + lo g_{10} (12 + x) = 2 + lo g_{10} (12 + x)

Simplify

lo g_{10} (4 x) = 2 + lo g_{10} (12 + x)

Apply log rules

4 x = 100 (12 + x)

Solve

4 x = 100 (12 + x) : x = \frac{19600 + 292000000}{32}

x = \frac{19600 + 292000000}{32}

Verify Solutions:

x = \frac{19600 + 292000000}{32}

True

The solution is

x = \frac{19600 + 292000000}{32}

lo g_{10} (x) = 1.75

lo g_{8} (5 x + 2) = \frac{1}{3}

y, ln (x^{2} - 8 y) = x - y - 2

lo g_{25} (3 x - 1) = \frac{1}{2}

lo g_{2} (2 x + 3) = 3

What is the answer to log_{10}(4x)-log_{10}(12+sqrt(x))=2 ?
The answer to log_{10}(4x)-log_{10}(12+sqrt(x))=2 is x=(19600+sqrt(292000000))/(32)
Solve for x: log_{10}(4x)-log_{10}(12+sqrt(x))=2
The solution is x=(19600+sqrt(292000000))/(32)