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

The answer to log_{3}(x+1)-log_{3}(x)=3 is x= 1/26

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

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

x = \frac{1}{26}

Decimal Notation

x = 0.03846 \dots

Solution steps

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

Add

lo g_{3} (x)

to both sides

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

Simplify

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

Apply log rules

x + 1 = 27 x

Solve

x + 1 = 27 x : x = \frac{1}{26}

x = \frac{1}{26}

Verify Solutions:

x = \frac{1}{26}

True

The solution is

x = \frac{1}{26}

lo g_{6} (x + 1) + lo g_{6} (x) = 1

lo g_{2} (x) = (lo g_{2} (x))^{2}

8 ln (x - 9) = 1

lo g_{3} (x) = lo g_{9} (2 x - 1)

ln (x + 7) + ln (x - 4) = 2 ln (x)

What is the answer to log_{3}(x+1)-log_{3}(x)=3 ?
The answer to log_{3}(x+1)-log_{3}(x)=3 is x= 1/26
Solve for x: log_{3}(x+1)-log_{3}(x)=3
The solution is x= 1/26