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

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

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

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

a = 2

Solution steps

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

Add

lo g_{5} (a - 1)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

a = 2, a = - 4

Verify Solutions:

a = 2

True

, a = - 4

False

The solution is

a = 2

50 = 10 lo g_{10} (x)

lo g_{11} (x) = - 1

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

5 + ln (x - 3) = 4

0 = ln (- c)

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