What is the answer to log_{10}((x+9)/x)=2 ?

The answer to log_{10}((x+9)/x)=2 is x= 1/11

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log_{10}((x+9)/x)=2

lo g_{10} (\frac{x + 9}{x}) = 2

x = \frac{1}{11}

Solution steps

lo g_{10} (\frac{x + 9}{x}) = 2

Apply log rules

\frac{x + 9}{x} = 1 0^{2}

Multiply both sides by

x

\frac{x + 9}{x} x = 1 0^{2} x

Simplify

x + 9 = 100 x

Solve

x + 9 = 100 x : x = \frac{1}{11}

x = \frac{1}{11}

Verify Solutions:

x = \frac{1}{11}

True

The solution is

x = \frac{1}{11}

lo g_{3} (x^{2} - 3 x - 7) = 1

y, x = lo g_{e} (y - 2)

lo g_{4} (x) - lo g_{4} (x - 2) = 2

- ln (1 - p) = 0.002

lo g_{6} (x - 2) = 4 + lo g_{6} (x + 2)

What is the answer to log_{10}((x+9)/x)=2 ?
The answer to log_{10}((x+9)/x)=2 is x= 1/11
Solve for x: log_{10}((x+9)/x)=2
The solution is x= 1/11