What is the answer to log_{10}(2x)-log_{10}(x-4)=1 ?

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

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log_{10}(2x)-log_{10}(x-4)=1

lo g_{10} (2 x) - lo g_{10} (x - 4) = 1

x = 5

Solution steps

lo g_{10} (2 x) - lo g_{10} (x - 4) = 1

Add

lo g_{10} (x - 4)

to both sides

lo g_{10} (2 x) - lo g_{10} (x - 4) + lo g_{10} (x - 4) = 1 + lo g_{10} (x - 4)

Simplify

lo g_{10} (2 x) = 1 + lo g_{10} (x - 4)

Apply log rules

2 x = 10 (x - 4)

Solve

2 x = 10 (x - 4) : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

ln (x) = 0.24

ln (x) = 0.23

3 ln (x + 4) = 6

ln (x) = 0.46

x, lo g_{p} (x) = 3

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