What is the answer to log_{5}(x)=3-log_{5}(x+20) ?

The answer to log_{5}(x)=3-log_{5}(x+20) is x=5

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log_{5}(x)=3-log_{5}(x+20)

lo g_{5} (x) = 3 - lo g_{5} (x + 20)

x = 5

Solution steps

lo g_{5} (x) = 3 - lo g_{5} (x + 20)

Add

lo g_{5} (x + 20)

to both sides

lo g_{5} (x) + lo g_{5} (x + 20) = 3 - lo g_{5} (x + 20) + lo g_{5} (x + 20)

Simplify

lo g_{5} (x) + lo g_{5} (x + 20) = 3

Apply log rules

x (x + 20) = 125

Solve

x (x + 20) = 125 : x = 5, x = - 25

x = 5, x = - 25

Verify Solutions:

x = 5

True

, x = - 25

False

The solution is

x = 5

2 - 2.12 = lo g_{10} (x)

- 35.5 = 10 lo g_{10} (\frac{x}{1})

lo g_{10} (2 + x) = 1

lo g_{4} (5 x + 7) - lo g_{4} (x - 3) = 2

lo g_{10} (x + 2) = 0

What is the answer to log_{5}(x)=3-log_{5}(x+20) ?
The answer to log_{5}(x)=3-log_{5}(x+20) is x=5
Solve for x: log_{5}(x)=3-log_{5}(x+20)
The solution is x=5