What is the answer to log_{5}(x-6)=-log_{5}(x-2)+1 ?

The answer to log_{5}(x-6)=-log_{5}(x-2)+1 is x=7

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log_{5}(x-6)=-log_{5}(x-2)+1

lo g_{5} (x - 6) = - lo g_{5} (x - 2) + 1

x = 7

Solution steps

lo g_{5} (x - 6) = - lo g_{5} (x - 2) + 1

Add

lo g_{5} (x - 2)

to both sides

lo g_{5} (x - 6) + lo g_{5} (x - 2) = - lo g_{5} (x - 2) + 1 + lo g_{5} (x - 2)

Simplify

lo g_{5} (x - 6) + lo g_{5} (x - 2) = 1

Apply log rules

(x - 6) (x - 2) = 5

Solve

(x - 6) (x - 2) = 5 : x = 7, x = 1

x = 7, x = 1

Verify Solutions:

x = 7

True

, x = 1

False

The solution is

x = 7

lo g_{5} (x - 4) = - 3

lo g_{2} (x - 3) + lo g_{2} (x - 2) = 1

ln (t - 2) = ln (8) - ln (t)

lo g_{10} (4 x) = lo g_{10} (7)

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

What is the answer to log_{5}(x-6)=-log_{5}(x-2)+1 ?
The answer to log_{5}(x-6)=-log_{5}(x-2)+1 is x=7
Solve for x: log_{5}(x-6)=-log_{5}(x-2)+1
The solution is x=7