What is the answer to log_{10}(x)-log_{10}(x-5)=1 ?

The answer to log_{10}(x)-log_{10}(x-5)=1 is x= 50/9

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log_{10}(x)-log_{10}(x-5)=1

lo g_{10} (x) - lo g_{10} (x - 5) = 1

x = \frac{50}{9}

Decimal Notation

x = 5.55555 \dots

Solution steps

lo g_{10} (x) - lo g_{10} (x - 5) = 1

Add

lo g_{10} (x - 5)

to both sides

lo g_{10} (x) - lo g_{10} (x - 5) + lo g_{10} (x - 5) = 1 + lo g_{10} (x - 5)

Simplify

lo g_{10} (x) = 1 + lo g_{10} (x - 5)

Apply log rules

x = 10 (x - 5)

Solve

x = 10 (x - 5) : x = \frac{50}{9}

x = \frac{50}{9}

Verify Solutions:

x = \frac{50}{9}

True

The solution is

x = \frac{50}{9}

x, ln (x) = y^{2}

lo g_{10} (5 x) = 4

5 ln (6 x + 9) + 20 = 5

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

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

What is the answer to log_{10}(x)-log_{10}(x-5)=1 ?
The answer to log_{10}(x)-log_{10}(x-5)=1 is x= 50/9
Solve for x: log_{10}(x)-log_{10}(x-5)=1
The solution is x= 50/9