What is the answer to log_{10}(6-2x)-log_{10}(x)=2 ?

The answer to log_{10}(6-2x)-log_{10}(x)=2 is x= 1/17

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log_{10}(6-2x)-log_{10}(x)=2

lo g_{10} (6 - 2 x) - lo g_{10} (x) = 2

x = \frac{1}{17}

Decimal Notation

x = 0.05882 \dots

Solution steps

lo g_{10} (6 - 2 x) - lo g_{10} (x) = 2

Add

lo g_{10} (x)

to both sides

lo g_{10} (6 - 2 x) - lo g_{10} (x) + lo g_{10} (x) = 2 + lo g_{10} (x)

Simplify

lo g_{10} (6 - 2 x) = 2 + lo g_{10} (x)

Apply log rules

6 - 2 x = 100 x

Solve

6 - 2 x = 100 x : x = \frac{1}{17}

x = \frac{1}{17}

Verify Solutions:

x = \frac{1}{17}

True

The solution is

x = \frac{1}{17}

lo g_{10} (t + 3) + lo g_{10} (t) = 1

lo g_{10} (x) + lo g_{10} (x - 4) = 1

ln (x) = 1 - 3 ln (2)

lo g_{8} (x + 30) + lo g_{8} (x) = 2

x, ln (y) = - 3 ln (x)

What is the answer to log_{10}(6-2x)-log_{10}(x)=2 ?
The answer to log_{10}(6-2x)-log_{10}(x)=2 is x= 1/17
Solve for x: log_{10}(6-2x)-log_{10}(x)=2
The solution is x= 1/17