What is the answer to log_{3}(x+4)-log_{3}(x-1)=2 ?

The answer to log_{3}(x+4)-log_{3}(x-1)=2 is x= 13/8

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log_{3}(x+4)-log_{3}(x-1)=2

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

x = \frac{13}{8}

Decimal Notation

x = 1.625

Solution steps

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

Add

lo g_{3} (x - 1)

to both sides

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

Simplify

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

Apply log rules

x + 4 = 9 (x - 1)

Solve

x + 4 = 9 (x - 1) : x = \frac{13}{8}

x = \frac{13}{8}

Verify Solutions:

x = \frac{13}{8}

True

The solution is

x = \frac{13}{8}

r, w = ln (1 + rs)

8 + lo g_{5} (- 4 x) = 10

7.4 = - lo g_{10} (x)

lo g_{2} (x) = - 2

lo g_{5} (x) = 16 lo g_{x} (5)

What is the answer to log_{3}(x+4)-log_{3}(x-1)=2 ?
The answer to log_{3}(x+4)-log_{3}(x-1)=2 is x= 13/8
Solve for x: log_{3}(x+4)-log_{3}(x-1)=2
The solution is x= 13/8