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

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

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

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

x = \frac{1}{9}

Decimal Notation

x = 0.11111 \dots

Solution steps

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

Apply log rules

10 x = x + 1

Solve

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

x = \frac{1}{9}

Verify Solutions:

x = \frac{1}{9}

True

The solution is

x = \frac{1}{9}

ln (x - 2) + ln (x + 2) = ln (3 x)

lo g_{9} (x + 1) - lo g_{9} (1 - x) = lo g_{9} (2 x + 3)

u, ln (1 - u) = x

ln (ln (x)) = 1

2 \cdot ln (x) + ln (x^{2} + 2) = ln (3)

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