What is the answer to log_{3}(x-8)-2=-log_{3}(x) ?

The answer to log_{3}(x-8)-2=-log_{3}(x) is x=9

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log_{3}(x-8)-2=-log_{3}(x)

lo g_{3} (x - 8) - 2 = - lo g_{3} (x)

x = 9

Solution steps

lo g_{3} (x - 8) - 2 = - lo g_{3} (x)

Add

lo g_{3} (x)

to both sides

lo g_{3} (x - 8) - 2 + lo g_{3} (x) = - lo g_{3} (x) + lo g_{3} (x)

Simplify

lo g_{3} (x - 8) - 2 + lo g_{3} (x) = 0

Apply log rules

(x - 8) x = 9

Solve

(x - 8) x = 9 : x = 9, x = - 1

x = 9, x = - 1

Verify Solutions:

x = 9

True

, x = - 1

False

The solution is

x = 9

ln (2 y + 5) = 2 + ln (4 - y)

0.78 = lo g_{10} (x)

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

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

lo g_{e} (x + 2) - lo g_{e} (3 x) = 0

What is the answer to log_{3}(x-8)-2=-log_{3}(x) ?
The answer to log_{3}(x-8)-2=-log_{3}(x) is x=9
Solve for x: log_{3}(x-8)-2=-log_{3}(x)
The solution is x=9