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

The answer to log_{3}(x)-log_{3}(2x-3)=3 is x= 81/53

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

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

x = \frac{81}{53}

Decimal

x = 1.52830 \dots

Solution steps

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

Add

lo g_{3} (2 x - 3)

to both sides

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

Simplify

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

Apply log rules

x = 27 (2 x - 3)

Solve

x = 27 (2 x - 3) : x = \frac{81}{53}

x = \frac{81}{53}

Verify Solutions:

x = \frac{81}{53}

True

The solution is

x = \frac{81}{53}

7.1 = - lo g_{10} (x)

ln (x) = m x

lo g_{2} (5 x) = 2

lo g_{2} (5 x) = 5

lo g_{0.5} (x) = 1

What is the answer to log_{3}(x)-log_{3}(2x-3)=3 ?
The answer to log_{3}(x)-log_{3}(2x-3)=3 is x= 81/53
Solve for x: log_{3}(x)-log_{3}(2x-3)=3
The solution is x= 81/53