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

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

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

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

x = 8

Solution steps

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

Add

lo g_{5} (x - 7)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = 8, x = 2

Verify Solutions:

x = 8

True

, x = 2

False

The solution is

x = 8

2 lo g_{2} (x) - lo g_{2} (2 x) = 3

2 ln (x) = ln (3) + ln (6 - x)

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

lo g_{2} (x) + lo g_{2} (- 4 x + 12) = 3

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

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