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=25

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

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

x = 25

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 = 25, x = - 5

x = 25, x = - 5

Verify Solutions:

x = 25

True

, x = - 5

False

The solution is

x = 25

k = lo g_{2} (k) + 1

lo g_{\frac{1}{2}} (x) = 1024

ln (2 x + 5) = 0

lo g_{10} (a) + lo g_{a} (100) = 3

ln (lo g_{10} (ln (x))) = 0.2

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=25
Solve for x: log_{5}(x)=3-log_{5}(x-20)
The solution is x=25