What is the answer to log_{10}(x+6)-log_{10}(x-3)=log_{10}(4) ?

The answer to log_{10}(x+6)-log_{10}(x-3)=log_{10}(4) is x=6

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log_{10}(x+6)-log_{10}(x-3)=log_{10}(4)

lo g_{10} (x + 6) - lo g_{10} (x - 3) = lo g_{10} (4)

x = 6

Solution steps

lo g_{10} (x + 6) - lo g_{10} (x - 3) = lo g_{10} (4)

Add

lo g_{10} (x - 3)

to both sides

lo g_{10} (x + 6) - lo g_{10} (x - 3) + lo g_{10} (x - 3) = lo g_{10} (4) + lo g_{10} (x - 3)

Simplify

lo g_{10} (x + 6) = lo g_{10} (4) + lo g_{10} (x - 3)

Apply log rules

x + 6 = 4 (x - 3)

Solve

x + 6 = 4 (x - 3) : x = 6

x = 6

Verify Solutions:

x = 6

True

The solution is

x = 6

ln (x) = 5 - x

lo g_{9} (x) = \frac{5}{2}

6.27 = - lo g_{10} (h)

ln (y) = 2

lo g_{10} (100 x) = \frac{1}{2}

What is the answer to log_{10}(x+6)-log_{10}(x-3)=log_{10}(4) ?
The answer to log_{10}(x+6)-log_{10}(x-3)=log_{10}(4) is x=6
Solve for x: log_{10}(x+6)-log_{10}(x-3)=log_{10}(4)
The solution is x=6