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

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

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

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

x = 7

Solution steps

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

Add

lo g_{5} (x - 2)

to both sides

lo g_{5} (x - 6) + lo g_{5} (x - 2) = 1 - lo g_{5} (x - 2) + 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_{6} (x) + lo g_{6} (x - 9) = 2

ln (x) = 2.5

e^{l n (x^{2})} + x = 6

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

lo g_{10} (x) - lo g_{10} (6) = 2

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