What is the answer to log_{8}(16)-log_{8}(x-2)=2 ?

The answer to log_{8}(16)-log_{8}(x-2)=2 is x= 9/4

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log_{8}(16)-log_{8}(x-2)=2

lo g_{8} (16) - lo g_{8} (x - 2) = 2

x = \frac{9}{4}

Solution steps

lo g_{8} (16) - lo g_{8} (x - 2) = 2

Move

lo g_{8} (16)

to the right side

- lo g_{8} (x - 2) = 2 - lo g_{8} (16)

Divide both sides by

- 1

lo g_{8} (x - 2) = - 2 + lo g_{8} (16)

Apply log rules

x - 2 = 8^{- 2 + \frac{4}{3}}

Solve

x - 2 = 8^{- 2 + \frac{4}{3}} : x = \frac{9}{4}

x = \frac{9}{4}

Verify Solutions:

x = \frac{9}{4}

True

The solution is

x = \frac{9}{4}

ln (x + 2) - ln (x) = ln (12)

5 lo g_{2} (x) = 10

lo g_{5} (y) = 2

lo g_{x} (128) = - 7

x, ln (x) = y + a

What is the answer to log_{8}(16)-log_{8}(x-2)=2 ?
The answer to log_{8}(16)-log_{8}(x-2)=2 is x= 9/4
Solve for x: log_{8}(16)-log_{8}(x-2)=2
The solution is x= 9/4