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

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

Solve for x: ((log_{10}(x)))/((log_{10)(x)+1)}=-1

The solution is x= 1/(sqrt(10))

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\frac{( lo g _{10} ( x ) )}{( lo g _{10} ( x ) + 1 )} = - 1

x = \frac{1}{10}

Decimal Notation

x = 0.31622 \dots

Solution steps

\frac{( lo g _{10} ( x ) )}{( lo g _{10} ( x ) + 1 )} = - 1

Multiply both sides by

lo g_{10} (x) + 1

\frac{lo g _{10} ( x )}{lo g _{10} ( x ) + 1} (lo g_{10} (x) + 1) = - 1 \cdot (lo g_{10} (x) + 1)

Simplify

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

Expand

- (lo g_{10} (x) + 1) : - lo g_{10} (x) - 1

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

Move

lo g_{10} (x)

to the left side

2 lo g_{10} (x) = - 1

Divide both sides by

2

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

Apply log rules

x = \frac{1}{10}

Verify Solutions:

x = \frac{1}{10}

True

The solution is

x = \frac{1}{10}

lo g_{5} ((2 x + 3)^{2}) - lo g_{5} (x) = 2

lo g_{3} (lo g_{5} (x - 2)) = - 1

lo g_{10} (x) = 1 - lo g_{10} (x - 3)

ln (x) + ln (x - 4) = ln (4)

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

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