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

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

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

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

x = 7

Solution steps

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

Add

lo g_{5} (x - 6)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 7, x = 1

Verify Solutions:

x = 7

True

, x = 1

False

The solution is

x = 7

lo g_{2} (x + 1) - lo g_{2} (x - 4) = 3

(lo g_{4} (1 + x^{2}))^{2} = 0.25

lo g_{5} (x + 3) = 1

lo g_{3} (x + 2) = lo g_{3} (5)

ln (x - 1) = 0

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