What is the answer to log_{5}(x-7)=1-log_{5}(x-3) ?

The answer to log_{5}(x-7)=1-log_{5}(x-3) is x=8

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log_{5}(x-7)=1-log_{5}(x-3)

lo g_{5} (x - 7) = 1 - lo g_{5} (x - 3)

x = 8

Solution steps

lo g_{5} (x - 7) = 1 - lo g_{5} (x - 3)

Add

lo g_{5} (x - 3)

to both sides

lo g_{5} (x - 7) + lo g_{5} (x - 3) = 1 - lo g_{5} (x - 3) + lo g_{5} (x - 3)

Simplify

lo g_{5} (x - 7) + lo g_{5} (x - 3) = 1

Apply log rules

(x - 7) (x - 3) = 5

Solve

(x - 7) (x - 3) = 5 : x = 8, x = 2

x = 8, x = 2

Verify Solutions:

x = 8

True

, x = 2

False

The solution is

x = 8

ln (x) + ln (x) = 0

lo g_{x} (9) = \frac{2}{3}

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

ln (x) - ln (\frac{1}{x}) = 2

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

What is the answer to log_{5}(x-7)=1-log_{5}(x-3) ?
The answer to log_{5}(x-7)=1-log_{5}(x-3) is x=8
Solve for x: log_{5}(x-7)=1-log_{5}(x-3)
The solution is x=8