What is the answer to log_{10}(x)-log_{10}(x+6)=-1 ?

The answer to log_{10}(x)-log_{10}(x+6)=-1 is x= 2/3

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log_{10}(x)-log_{10}(x+6)=-1

lo g_{10} (x) - lo g_{10} (x + 6) = - 1

x = \frac{2}{3}

Decimal Notation

x = 0.66666 \dots

Solution steps

lo g_{10} (x) - lo g_{10} (x + 6) = - 1

Add

lo g_{10} (x + 6)

to both sides

lo g_{10} (x) - lo g_{10} (x + 6) + lo g_{10} (x + 6) = - 1 + lo g_{10} (x + 6)

Simplify

lo g_{10} (x) = - 1 + lo g_{10} (x + 6)

Apply log rules

x \cdot 10 = x + 6

Solve

x \cdot 10 = x + 6 : x = \frac{2}{3}

x = \frac{2}{3}

Verify Solutions:

x = \frac{2}{3}

True

The solution is

x = \frac{2}{3}

lo g_{2} (x) = - 2

ln (3 x - 11) = 6

0.66 = ln (x)

x, - 4 lo g_{2} (5 x) = - 12

e^{l n (x^{2})} = x^{2}

What is the answer to log_{10}(x)-log_{10}(x+6)=-1 ?
The answer to log_{10}(x)-log_{10}(x+6)=-1 is x= 2/3
Solve for x: log_{10}(x)-log_{10}(x+6)=-1
The solution is x= 2/3