What is the answer to log_{6}(x-8)=2-log_{6}(x+8) ?

The answer to log_{6}(x-8)=2-log_{6}(x+8) is x=10

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log_{6}(x-8)=2-log_{6}(x+8)

lo g_{6} (x - 8) = 2 - lo g_{6} (x + 8)

x = 10

Solution steps

lo g_{6} (x - 8) = 2 - lo g_{6} (x + 8)

Add

lo g_{6} (x + 8)

to both sides

lo g_{6} (x - 8) + lo g_{6} (x + 8) = 2 - lo g_{6} (x + 8) + lo g_{6} (x + 8)

Simplify

lo g_{6} (x - 8) + lo g_{6} (x + 8) = 2

Apply log rules

(x - 8) (x + 8) = 36

Solve

(x - 8) (x + 8) = 36 : x = 10, x = - 10

x = 10, x = - 10

Verify Solutions:

x = 10

True

, x = - 10

False

The solution is

x = 10

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

lo g_{3} (8 x + 9) = 4

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

ln (2 x + 1) + ln (x + 1) = 0

2.5 = - lo g_{10} (x)

What is the answer to log_{6}(x-8)=2-log_{6}(x+8) ?
The answer to log_{6}(x-8)=2-log_{6}(x+8) is x=10
Solve for x: log_{6}(x-8)=2-log_{6}(x+8)
The solution is x=10