What is the answer to log_{3}(x-2)+log_{3}(x-4)=2 ?

The answer to log_{3}(x-2)+log_{3}(x-4)=2 is x=3+sqrt(10)

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log_{3}(x-2)+log_{3}(x-4)=2

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

x = 3 + 10

Decimal Notation

x = 6.16227 \dots

Solution steps

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

Apply log rules

(x - 2) (x - 4) = 9

Solve

(x - 2) (x - 4) = 9 : x = 3 + 10, x = 3 - 10

x = 3 + 10, x = 3 - 10

Verify Solutions:

x = 3 + 10

True

, x = 3 - 10

False

The solution is

x = 3 + 10

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

4 ln (4 b) = ln (2 b)

ln (x) + ln (x - 6) = 1

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

x, ln (x) = 2

What is the answer to log_{3}(x-2)+log_{3}(x-4)=2 ?
The answer to log_{3}(x-2)+log_{3}(x-4)=2 is x=3+sqrt(10)
Solve for x: log_{3}(x-2)+log_{3}(x-4)=2
The solution is x=3+sqrt(10)