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

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

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

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

x = - 1

Solution steps

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

Add

lo g_{5} (x + 2)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = - 1, x = - 7

Verify Solutions:

x = - 1

True

, x = - 7

False

The solution is

x = - 1

lo g_{a} (3) = 4

lo g_{7} (x) + lo g_{8} (x) = 1

ln (x + 7) = 2

2 lo g_{8} (5) = lo g_{8} (x)

lo g_{e} (x^{2}) + lo g_{7} (x) = 2

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