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

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

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

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

x = \frac{1}{11}

Decimal Notation

x = 0.09090 \dots

Solution steps

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

Apply log rules

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} (- 2 x + 8) = 1

lo g_{10} (x - 2) = 3

2 lo g_{4} (x) + lo g_{x} (4) = 3

lo g_{4} (x) + lo g_{4} (x - 3) = 1

lo g_{6} (2 x) - lo g_{6} (x + 1) = 0

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