What is the answer to log_{3}(10)-log_{3}(-2x)=4 ?

The answer to log_{3}(10)-log_{3}(-2x)=4 is x=-5/81

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log_{3}(10)-log_{3}(-2x)=4

lo g_{3} (10) - lo g_{3} (- 2 x) = 4

x = - \frac{5}{81}

Solution steps

lo g_{3} (10) - lo g_{3} (- 2 x) = 4

Move

lo g_{3} (10)

to the right side

- lo g_{3} (- 2 x) = 4 - lo g_{3} (10)

Divide both sides by

- 1

lo g_{3} (- 2 x) = - 4 + lo g_{3} (10)

Apply log rules

- 2 x = \frac{10}{81}

Solve

- 2 x = \frac{10}{81} : x = - \frac{5}{81}

x = - \frac{5}{81}

Verify Solutions:

x = - \frac{5}{81}

True

The solution is

x = - \frac{5}{81}

lo g_{3} (8 x - 2) + lo g_{3} (x - 1) = 2

lo g_{5} (X) = - 2

ln (3 x + e) = 3

ln (x^{7}) - ln (x^{4}) = 3

2 = lo g_{b} (900)

What is the answer to log_{3}(10)-log_{3}(-2x)=4 ?
The answer to log_{3}(10)-log_{3}(-2x)=4 is x=-5/81
Solve for x: log_{3}(10)-log_{3}(-2x)=4
The solution is x=-5/81