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

The answer to log_{6}(x)=2-log_{6}(x-5) is x=9

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

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

x = 9

Solution steps

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

Add

lo g_{6} (x - 5)

to both sides

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

Simplify

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

Apply log rules

x (x - 5) = 36

Solve

x (x - 5) = 36 : x = 9, x = - 4

x = 9, x = - 4

Verify Solutions:

x = 9

True

, x = - 4

False

The solution is

x = 9

lo g_{9} (8 x - 15) = 0

x, y = 10 lo g_{10} (x)

lo g_{5} (k) = - 1

- 6 lo g_{5} (x) = 12

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

What is the answer to log_{6}(x)=2-log_{6}(x-5) ?
The answer to log_{6}(x)=2-log_{6}(x-5) is x=9
Solve for x: log_{6}(x)=2-log_{6}(x-5)
The solution is x=9