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

The answer to log_{10}(x)+log_{10}(x+4)=1 is x=-2+sqrt(14)

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log_{10}(x)+log_{10}(x+4)=1

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

x = - 2 + 14

Decimal Notation

x = 1.74165 \dots

Solution steps

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

Apply log rules

x (x + 4) = 10

Solve

x (x + 4) = 10 : x = - 2 + 14, x = - 2 - 14

x = - 2 + 14, x = - 2 - 14

Verify Solutions:

x = - 2 + 14

True

, x = - 2 - 14

False

The solution is

x = - 2 + 14

ln (x) = 6 + 2 ln (2)

lo g_{4} (5 x + 2) = 5 x

- lo g_{10} (x) = 7.4

- lo g_{10} (x) = 7.1

x (lo g_{10} (x) + 1)^{2} = 0

What is the answer to log_{10}(x)+log_{10}(x+4)=1 ?
The answer to log_{10}(x)+log_{10}(x+4)=1 is x=-2+sqrt(14)
Solve for x: log_{10}(x)+log_{10}(x+4)=1
The solution is x=-2+sqrt(14)