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

The answer to log_{5}(x+7)=1-log_{5}(x+3) is x=-2

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

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

x = - 2

Solution steps

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

Add

lo g_{5} (x + 3)

to both sides

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

Simplify

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

Apply log rules

(x + 7) (x + 3) = 5

Solve

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

x = - 2, x = - 8

Verify Solutions:

x = - 2

True

, x = - 8

False

The solution is

x = - 2

lo g_{7} (x) = - 2

4 = lo g_{2} (x)

- 2 lo g_{3} (4 x) = - 6

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

lo g_{4} (x) = 9

What is the answer to log_{5}(x+7)=1-log_{5}(x+3) ?
The answer to log_{5}(x+7)=1-log_{5}(x+3) is x=-2
Solve for x: log_{5}(x+7)=1-log_{5}(x+3)
The solution is x=-2