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

The answer to log_{3}(x+2)=2-log_{3}(3x) is x=1

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

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

x = 1

Solution steps

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

Add

lo g_{3} (3 x)

to both sides

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

Simplify

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

Apply log rules

(x + 2) \cdot 3 x = 9

Solve

(x + 2) \cdot 3 x = 9 : x = 1, x = - 3

x = 1, x = - 3

Verify Solutions:

x = 1

True

, x = - 3

False

The solution is

x = 1

ln (3 x + 4) - ln (2 x + 1) = 5

lo g_{3} (lo g_{5} (x^{2})) = 1

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

lo g_{10} (x) 9 = 2

lo g_{10} (x - 1) = 0

What is the answer to log_{3}(x+2)=2-log_{3}(3x) ?
The answer to log_{3}(x+2)=2-log_{3}(3x) is x=1
Solve for x: log_{3}(x+2)=2-log_{3}(3x)
The solution is x=1