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

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

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

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

x = 3 + 10

Decimal Notation

x = 6.16227 \dots

Solution steps

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

Add

lo g_{3} (x - 4)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

1.9 = - lo g_{10} (x)

lo g_{2} (x + 6) + lo g_{2} (x) = 4

lo g_{3} (2 x) = 4

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

lo g_{2} (2 x + 6) - lo g_{2} (x) = 3

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