What is the answer to log_{5}(x-8)=1-log_{5}(x-4) ?

The answer to log_{5}(x-8)=1-log_{5}(x-4) is x=9

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log_{5}(x-8)=1-log_{5}(x-4)

lo g_{5} (x - 8) = 1 - lo g_{5} (x - 4)

x = 9

Solution steps

lo g_{5} (x - 8) = 1 - lo g_{5} (x - 4)

Add

lo g_{5} (x - 4)

to both sides

lo g_{5} (x - 8) + lo g_{5} (x - 4) = 1 - lo g_{5} (x - 4) + lo g_{5} (x - 4)

Simplify

lo g_{5} (x - 8) + lo g_{5} (x - 4) = 1

Apply log rules

(x - 8) (x - 4) = 5

Solve

(x - 8) (x - 4) = 5 : x = 9, x = 3

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

False

The solution is

x = 9

lo g_{8} (x) = - 2

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

lo g_{5} (x - 2) = lo g_{5} (3 x + 7)

lo g_{10} (x) + lo g_{10} (3) = 1

lo g_{x} (7 x - 10) = 2

What is the answer to log_{5}(x-8)=1-log_{5}(x-4) ?
The answer to log_{5}(x-8)=1-log_{5}(x-4) is x=9
Solve for x: log_{5}(x-8)=1-log_{5}(x-4)
The solution is x=9