What is the answer to log_{6}(x)=1-log_{6}(x+5) ?

The answer to log_{6}(x)=1-log_{6}(x+5) is x=1

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log_{6}(x)=1-log_{6}(x+5)

lo g_{6} (x) = 1 - lo g_{6} (x + 5)

x = 1

Solution steps

lo g_{6} (x) = 1 - lo g_{6} (x + 5)

Add

lo g_{6} (x + 5)

to both sides

lo g_{6} (x) + lo g_{6} (x + 5) = 1 - lo g_{6} (x + 5) + lo g_{6} (x + 5)

Simplify

lo g_{6} (x) + lo g_{6} (x + 5) = 1

Apply log rules

x (x + 5) = 6

Solve

x (x + 5) = 6 : x = 1, x = - 6

x = 1, x = - 6

Verify Solutions:

x = 1

True

, x = - 6

False

The solution is

x = 1

lo g_{5} (\frac{x}{x - 8}) = 3

lo g_{4 x} (5) = 3

ln (x) + ln (\frac{1}{x} + 1) = 3

x, ln (ln (x)) = 0

lo g_{x} (336) = 2

What is the answer to log_{6}(x)=1-log_{6}(x+5) ?
The answer to log_{6}(x)=1-log_{6}(x+5) is x=1
Solve for x: log_{6}(x)=1-log_{6}(x+5)
The solution is x=1