What is the answer to log_{5}(x+2)=1-log_{5}(x+6) ?

The answer to log_{5}(x+2)=1-log_{5}(x+6) is x=-1

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log_{5}(x+2)=1-log_{5}(x+6)

lo g_{5} (x + 2) = 1 - lo g_{5} (x + 6)

x = - 1

Solution steps

lo g_{5} (x + 2) = 1 - lo g_{5} (x + 6)

Add

lo g_{5} (x + 6)

to both sides

lo g_{5} (x + 2) + lo g_{5} (x + 6) = 1 - lo g_{5} (x + 6) + lo g_{5} (x + 6)

Simplify

lo g_{5} (x + 2) + lo g_{5} (x + 6) = 1

Apply log rules

(x + 2) (x + 6) = 5

Solve

(x + 2) (x + 6) = 5 : x = - 1, x = - 7

x = - 1, x = - 7

Verify Solutions:

x = - 1

True

, x = - 7

False

The solution is

x = - 1

0.32 = ln (x)

9 ln (x) = 1

ln (x^{8}) - ln (x^{3}) = 5

2 ln (x - 1) = 0

lo g_{5} (x - 25) - lo g_{5} (x - 1) = 3

What is the answer to log_{5}(x+2)=1-log_{5}(x+6) ?
The answer to log_{5}(x+2)=1-log_{5}(x+6) is x=-1
Solve for x: log_{5}(x+2)=1-log_{5}(x+6)
The solution is x=-1