What is the answer to log_{10}(x)-log_{10}(x+3)=-1 ?

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

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log_{10}(x)-log_{10}(x+3)=-1

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

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

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

Add

lo g_{10} (x + 3)

to both sides

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

Simplify

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

Apply log rules

x \cdot 10 = x + 3

Solve

x \cdot 10 = x + 3 : x = \frac{1}{3}

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

x \cdot ln (x) = 0

ln (5 x + 1) + ln (x) = ln (4)

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

lo g_{\frac{1}{4}} (x) = 2

lo g_{2} (4 x) = 8 lo g_{x} (2)

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