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

The answer to log_{8}(x)-log_{8}(x-3)=2 is x= 64/21

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

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

x = \frac{64}{21}

Decimal Notation

x = 3.04761 \dots

Solution steps

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

Add

lo g_{8} (x - 3)

to both sides

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

Simplify

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

Apply log rules

x = 64 (x - 3)

Solve

x = 64 (x - 3) : x = \frac{64}{21}

x = \frac{64}{21}

Verify Solutions:

x = \frac{64}{21}

True

The solution is

x = \frac{64}{21}

lo g_{2 x - 3} (3 x^{2} - 18) = 2

4 ln (5 x - 4) - 11 = 5

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

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

lo g_{3} (x - 4) = 1 + lo g_{9} (x)

What is the answer to log_{8}(x)-log_{8}(x-3)=2 ?
The answer to log_{8}(x)-log_{8}(x-3)=2 is x= 64/21
Solve for x: log_{8}(x)-log_{8}(x-3)=2
The solution is x= 64/21