What is the answer to log_{10}(2x)-log_{10}(x-1)=1 ?

The answer to log_{10}(2x)-log_{10}(x-1)=1 is x= 5/4

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log_{10}(2x)-log_{10}(x-1)=1

lo g_{10} (2 x) - lo g_{10} (x - 1) = 1

x = \frac{5}{4}

Decimal Notation

x = 1.25

Solution steps

lo g_{10} (2 x) - lo g_{10} (x - 1) = 1

Add

lo g_{10} (x - 1)

to both sides

lo g_{10} (2 x) - lo g_{10} (x - 1) + lo g_{10} (x - 1) = 1 + lo g_{10} (x - 1)

Simplify

lo g_{10} (2 x) = 1 + lo g_{10} (x - 1)

Apply log rules

2 x = 10 (x - 1)

Solve

2 x = 10 (x - 1) : x = \frac{5}{4}

x = \frac{5}{4}

Verify Solutions:

x = \frac{5}{4}

True

The solution is

x = \frac{5}{4}

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

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

3 ln (4 x - 5) - 17 = - 5

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

2 lo g_{10} (x) = lo g_{10} (1)

What is the answer to log_{10}(2x)-log_{10}(x-1)=1 ?
The answer to log_{10}(2x)-log_{10}(x-1)=1 is x= 5/4
Solve for x: log_{10}(2x)-log_{10}(x-1)=1
The solution is x= 5/4