What is the answer to log_{3}(x)=3-log_{3}(x+6) ?

The answer to log_{3}(x)=3-log_{3}(x+6) is x=3

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log_{3}(x)=3-log_{3}(x+6)

lo g_{3} (x) = 3 - lo g_{3} (x + 6)

x = 3

Solution steps

lo g_{3} (x) = 3 - lo g_{3} (x + 6)

Add

lo g_{3} (x + 6)

to both sides

lo g_{3} (x) + lo g_{3} (x + 6) = 3 - lo g_{3} (x + 6) + lo g_{3} (x + 6)

Simplify

lo g_{3} (x) + lo g_{3} (x + 6) = 3

Apply log rules

x (x + 6) = 27

Solve

x (x + 6) = 27 : x = 3, x = - 9

x = 3, x = - 9

Verify Solutions:

x = 3

True

, x = - 9

False

The solution is

x = 3

1 = ln (y)

2 lo g_{2} (x + 2) - lo g_{2} (x + 1) = 2

lo g_{x} (4) = 4 lo g_{x} (x)

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

0 = 2 x ln (x) + x

What is the answer to log_{3}(x)=3-log_{3}(x+6) ?
The answer to log_{3}(x)=3-log_{3}(x+6) is x=3
Solve for x: log_{3}(x)=3-log_{3}(x+6)
The solution is x=3