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

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

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

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

x = - 2

Solution steps

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

Add

lo g_{5} (x + 7)

to both sides

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

Simplify

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

Apply log rules

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

Solve

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

x = - 2, x = - 8

Verify Solutions:

x = - 2

True

, x = - 8

False

The solution is

x = - 2

x, 4.83 = - lo g_{10} (x)

ln (- x + 1) - ln (3 x + 5) = ln (- 6 x + 1)

a = \frac{1}{2} a ln (x)

ln (x) = 0.9

lo g_{3} (4 x + 5) = 1

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