What is the answer to log_{3}(8x+1)-log_{3}(x-1)=2 ?

The answer to log_{3}(8x+1)-log_{3}(x-1)=2 is x=10

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

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

x = 10

Solution steps

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

Add

lo g_{3} (x - 1)

to both sides

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

Simplify

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

Apply log rules

8 x + 1 = 9 (x - 1)

Solve

8 x + 1 = 9 (x - 1) : x = 10

x = 10

Verify Solutions:

x = 10

True

The solution is

x = 10

5.6 = - lo g_{10} (x)

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

lo g_{0.02} (x) = - 1

13 ln (2 x + 3) = 15

lo g_{5} (x) = 2.6

What is the answer to log_{3}(8x+1)-log_{3}(x-1)=2 ?
The answer to log_{3}(8x+1)-log_{3}(x-1)=2 is x=10
Solve for x: log_{3}(8x+1)-log_{3}(x-1)=2
The solution is x=10