What is the answer to log_{10}(x+3)-log_{10}(x)=2 ?

The answer to log_{10}(x+3)-log_{10}(x)=2 is x= 1/33

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log_{10}(x+3)-log_{10}(x)=2

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

x = \frac{1}{33}

Decimal Notation

x = 0.03030 \dots

Solution steps

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

Add

lo g_{10} (x)

to both sides

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

Simplify

lo g_{10} (x + 3) = 2 + lo g_{10} (x)

Apply log rules

x + 3 = 100 x

Solve

x + 3 = 100 x : x = \frac{1}{33}

x = \frac{1}{33}

Verify Solutions:

x = \frac{1}{33}

True

The solution is

x = \frac{1}{33}

2 lo g_{10} (x) = 10

lo g_{2} (2 x + 7) = 3

2 ln (x) - 3 ln (\frac{1}{x}) = 10

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

ln (x + 1) = 8

What is the answer to log_{10}(x+3)-log_{10}(x)=2 ?
The answer to log_{10}(x+3)-log_{10}(x)=2 is x= 1/33
Solve for x: log_{10}(x+3)-log_{10}(x)=2
The solution is x= 1/33