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

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

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log_{10}(1+x)=1+log_{10}(x)

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

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

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

Apply log rules

1 + x = 10 x

Solve

1 + x = 10 x : x = \frac{1}{9}

x = \frac{1}{9}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

ln (x + 1) = - 2

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

lo g_{6} (2 x + 16) = 3

- 3.75 = lo g_{10} (y)

2 \cdot lo g_{10} (x) = lo g_{10} (2) + lo g_{10} (3 x - 4)

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