What is the answer to log_{10}((x^2)/(x-1))=3 ?

The answer to log_{10}((x^2)/(x-1))=3 is x=10(50+sqrt(2490)),x=10(50-sqrt(2490))

Solve for x: log_{10}((x^2)/(x-1))=3

The solution is x=10(50+sqrt(2490)),x=10(50-sqrt(2490))

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lo g_{10} (\frac{x ^{2}}{x - 1}) = 3

x = 10 (50 + 2490), x = 10 (50 - 2490)

Decimal Notation

x = 998.99899 \dots, x = 1.00100 \dots

Solution steps

lo g_{10} (\frac{x ^{2}}{x - 1}) = 3

Apply log rules

\frac{x ^{2}}{x - 1} = 1 0^{3}

Multiply both sides by

x - 1

\frac{x ^{2}}{x - 1} (x - 1) = 1 0^{3} (x - 1)

Simplify

x^{2} = 1000 (x - 1)

Solve

x^{2} = 1000 (x - 1) : x = 10 (50 + 2490), x = 10 (50 - 2490)

x = 10 (50 + 2490), x = 10 (50 - 2490)

Verify Solutions:

x = 10 (50 + 2490)

True

, x = 10 (50 - 2490)

True

The solutions are

x = 10 (50 + 2490), x = 10 (50 - 2490)

z^{2} - 2 z + i = 0

(x + y i)^{2} = 3 - 4 i

\frac{z - i}{z} = 2 + i

z^{2} = 3 + 4 i

(x - y i)^{2} = - 8 - 6 i

What is the answer to log_{10}((x^2)/(x-1))=3 ?
The answer to log_{10}((x^2)/(x-1))=3 is x=10(50+sqrt(2490)),x=10(50-sqrt(2490))
Solve for x: log_{10}((x^2)/(x-1))=3
The solution is x=10(50+sqrt(2490)),x=10(50-sqrt(2490))