What is the answer to log_{10}(x)-log_{10}(x-6)=4 ?

The answer to log_{10}(x)-log_{10}(x-6)=4 is x= 20000/3333

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log_{10}(x)-log_{10}(x-6)=4

lo g_{10} (x) - lo g_{10} (x - 6) = 4

x = \frac{20000}{3333}

Decimal Notation

x = 6.00060 \dots

Solution steps

lo g_{10} (x) - lo g_{10} (x - 6) = 4

Add

lo g_{10} (x - 6)

to both sides

lo g_{10} (x) - lo g_{10} (x - 6) + lo g_{10} (x - 6) = 4 + lo g_{10} (x - 6)

Simplify

lo g_{10} (x) = 4 + lo g_{10} (x - 6)

Apply log rules

x = 10000 (x - 6)

Solve

x = 10000 (x - 6) : x = \frac{20000}{3333}

x = \frac{20000}{3333}

Verify Solutions:

x = \frac{20000}{3333}

True

The solution is

x = \frac{20000}{3333}

ln ∣ x ∣ = x - 2

lo g_{6} (2 X + 3) = 3

1 = - lo g_{10} (t)

lo g_{x} (35) = 1

lo g_{10} (100 x) = 1.5

What is the answer to log_{10}(x)-log_{10}(x-6)=4 ?
The answer to log_{10}(x)-log_{10}(x-6)=4 is x= 20000/3333
Solve for x: log_{10}(x)-log_{10}(x-6)=4
The solution is x= 20000/3333