What is the answer to log_{3}(2x+9)-log_{3}(5x)=3 ?

The answer to log_{3}(2x+9)-log_{3}(5x)=3 is x= 9/133

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log_{3}(2x+9)-log_{3}(5x)=3

lo g_{3} (2 x + 9) - lo g_{3} (5 x) = 3

x = \frac{9}{133}

Decimal Notation

x = 0.06766 \dots

Solution steps

lo g_{3} (2 x + 9) - lo g_{3} (5 x) = 3

Add

lo g_{3} (5 x)

to both sides

lo g_{3} (2 x + 9) - lo g_{3} (5 x) + lo g_{3} (5 x) = 3 + lo g_{3} (5 x)

Simplify

lo g_{3} (2 x + 9) = 3 + lo g_{3} (5 x)

Apply log rules

2 x + 9 = 135 x

Solve

2 x + 9 = 135 x : x = \frac{9}{133}

x = \frac{9}{133}

Verify Solutions:

x = \frac{9}{133}

True

The solution is

x = \frac{9}{133}

2 lo g_{2} (x) + 5 = 21

lo g_{5} (x + 7) + lo g_{5} (x - 4) = 3

∣ ln (x + 3) ∣ = 1

lo g_{3} (4) + lo g_{3} (x) = 1

7.4 = lo g_{10} (x)

What is the answer to log_{3}(2x+9)-log_{3}(5x)=3 ?
The answer to log_{3}(2x+9)-log_{3}(5x)=3 is x= 9/133
Solve for x: log_{3}(2x+9)-log_{3}(5x)=3
The solution is x= 9/133