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

The answer to log_{10}(x)-log_{10}(x-3)=2 is x= 100/33

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

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

x = \frac{100}{33}

Decimal Notation

x = 3.03030 \dots

Solution steps

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

Add

lo g_{10} (x - 3)

to both sides

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

Simplify

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

Apply log rules

x = 100 (x - 3)

Solve

x = 100 (x - 3) : x = \frac{100}{33}

x = \frac{100}{33}

Verify Solutions:

x = \frac{100}{33}

True

The solution is

x = \frac{100}{33}

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

x, y = 4 \cdot ln (x + c)

2 = 2 x + ln (x)

lo g_{2} (x) - lo g_{4} (3 x + 4) = 0

ln (x) = ln (x)

What is the answer to log_{10}(x)-log_{10}(x-3)=2 ?
The answer to log_{10}(x)-log_{10}(x-3)=2 is x= 100/33
Solve for x: log_{10}(x)-log_{10}(x-3)=2
The solution is x= 100/33