What is the answer to log_{10}(2x)-log_{10}(x-3)=1 ?

The answer to log_{10}(2x)-log_{10}(x-3)=1 is x= 15/4

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log_{10}(2x)-log_{10}(x-3)=1

lo g_{10} (2 x) - lo g_{10} (x - 3) = 1

x = \frac{15}{4}

Decimal Notation

x = 3.75

Solution steps

lo g_{10} (2 x) - lo g_{10} (x - 3) = 1

Add

lo g_{10} (x - 3)

to both sides

lo g_{10} (2 x) - lo g_{10} (x - 3) + lo g_{10} (x - 3) = 1 + lo g_{10} (x - 3)

Simplify

lo g_{10} (2 x) = 1 + lo g_{10} (x - 3)

Apply log rules

2 x = 10 (x - 3)

Solve

2 x = 10 (x - 3) : x = \frac{15}{4}

x = \frac{15}{4}

Verify Solutions:

x = \frac{15}{4}

True

The solution is

x = \frac{15}{4}

ln (2 x) = 4

ln (x - 3) + ln (x - 2) = ln (2 x + 24)

lo g_{10} (5 x) = 2

ln (x^{2}) = 12

7 = - lo g_{10} (x)

What is the answer to log_{10}(2x)-log_{10}(x-3)=1 ?
The answer to log_{10}(2x)-log_{10}(x-3)=1 is x= 15/4
Solve for x: log_{10}(2x)-log_{10}(x-3)=1
The solution is x= 15/4