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

The answer to log_{5}(x+3)=1-log_{5}(x-1) is x=2

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

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

x = 2

Solution steps

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

Add

lo g_{5} (x - 1)

to both sides

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

Simplify

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

Apply log rules

(x + 3) (x - 1) = 5

Solve

(x + 3) (x - 1) = 5 : x = 2, x = - 4

x = 2, x = - 4

Verify Solutions:

x = 2

True

, x = - 4

False

The solution is

x = 2

3 lo g_{10} (x) = 3

ln (3 x) = 2

ln (6 x - 9) - 2 ln (x) = 0

ln (t) - ln (t + 1) = 2

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

What is the answer to log_{5}(x+3)=1-log_{5}(x-1) ?
The answer to log_{5}(x+3)=1-log_{5}(x-1) is x=2
Solve for x: log_{5}(x+3)=1-log_{5}(x-1)
The solution is x=2