What is the answer to log_{3}(x+6)-log_{3}(x)=2 ?

The answer to log_{3}(x+6)-log_{3}(x)=2 is x= 3/4

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log_{3}(x+6)-log_{3}(x)=2

lo g_{3} (x + 6) - lo g_{3} (x) = 2

x = \frac{3}{4}

Decimal Notation

x = 0.75

Solution steps

lo g_{3} (x + 6) - lo g_{3} (x) = 2

Add

lo g_{3} (x)

to both sides

lo g_{3} (x + 6) - lo g_{3} (x) + lo g_{3} (x) = 2 + lo g_{3} (x)

Simplify

lo g_{3} (x + 6) = 2 + lo g_{3} (x)

Apply log rules

x + 6 = 9 x

Solve

x + 6 = 9 x : x = \frac{3}{4}

x = \frac{3}{4}

Verify Solutions:

x = \frac{3}{4}

True

The solution is

x = \frac{3}{4}

lo g_{10} (x + 1) = 3

lo g_{4} (x - 1) = lo g_{2} (x - 3)

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

lo g_{3} (\frac{2 x - 3}{4}) = lo g_{3} (x + 1)

lo g_{10} (x + 2) - lo g_{10} (x + 1) = 1

What is the answer to log_{3}(x+6)-log_{3}(x)=2 ?
The answer to log_{3}(x+6)-log_{3}(x)=2 is x= 3/4
Solve for x: log_{3}(x+6)-log_{3}(x)=2
The solution is x= 3/4