What is the answer to log_{5}(8)-log_{5}(2x)=2 ?

The answer to log_{5}(8)-log_{5}(2x)=2 is x= 4/25

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log_{5}(8)-log_{5}(2x)=2

lo g_{5} (8) - lo g_{5} (2 x) = 2

x = \frac{4}{25}

Decimal Notation

x = 0.16

Solution steps

lo g_{5} (8) - lo g_{5} (2 x) = 2

Move

lo g_{5} (8)

to the right side

- lo g_{5} (2 x) = 2 - lo g_{5} (8)

Divide both sides by

- 1

lo g_{5} (2 x) = - 2 + lo g_{5} (8)

Apply log rules

2 x = \frac{8}{25}

Solve

2 x = \frac{8}{25} : x = \frac{4}{25}

x = \frac{4}{25}

Verify Solutions:

x = \frac{4}{25}

True

The solution is

x = \frac{4}{25}

x, ln (x) = t + ln (4)

lo g_{10} (x) = lo g_{10} (4)

lo g_{10} (x) + lo g_{10} (5) = 1

ln (x) = 1.8379

lo g_{e} (x) = 1.75

What is the answer to log_{5}(8)-log_{5}(2x)=2 ?
The answer to log_{5}(8)-log_{5}(2x)=2 is x= 4/25
Solve for x: log_{5}(8)-log_{5}(2x)=2
The solution is x= 4/25