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

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

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

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

x = 9

Solution steps

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

Add

lo g_{5} (x - 8)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 9, x = 3

Verify Solutions:

x = 9

True

, x = 3

False

The solution is

x = 9

ln (x + 2) + ln (x) = ln (6 x) - ln (6)

ln (x^{2}) = 0

ln (2 x + 3) = 1

lo g_{b} (3^{b}) = \frac{b}{2}

lo g_{10} (2 x + 1) = 3

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