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

The answer to 2log_{10}(x)=log_{10}(2x-3)+log_{10}(3) is x=3

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

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

x = 3

Solution steps

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

Apply log rules

x^{2} = (2 x - 3) \cdot 3

Solve

x^{2} = (2 x - 3) \cdot 3 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

lo g_{d} (3) = \frac{1}{2}

lo g_{10} (x) + lo g_{10} (x - 5) = lo g_{10} (6)

x, ln (x) = - 1

3 lo g_{3} (x) = 0

12 lo g_{10} (3 x) = 6

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