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

The answer to log_{3}(x)+log_{3}(x-4)=3 is x=2+sqrt(31)

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

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

x = 2 + 31

Decimal Notation

x = 7.56776 \dots

Solution steps

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

Apply log rules

x (x - 4) = 27

Solve

x (x - 4) = 27 : x = 2 + 31, x = 2 - 31

x = 2 + 31, x = 2 - 31

Verify Solutions:

x = 2 + 31

True

, x = 2 - 31

False

The solution is

x = 2 + 31

lo g_{b} (2) = 2.48

ln (x) = - 2 ln (5)

7.25 = - 2 lo g_{10} (2 x + 5)

lo g_{10} (3 x - 4) = 2

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

What is the answer to log_{3}(x)+log_{3}(x-4)=3 ?
The answer to log_{3}(x)+log_{3}(x-4)=3 is x=2+sqrt(31)
Solve for x: log_{3}(x)+log_{3}(x-4)=3
The solution is x=2+sqrt(31)