What is the answer to log_{4}(2)-log_{4}(2-5x)=4 ?

The answer to log_{4}(2)-log_{4}(2-5x)=4 is x= 51/128

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log_{4}(2)-log_{4}(2-5x)=4

lo g_{4} (2) - lo g_{4} (2 - 5 x) = 4

x = \frac{51}{128}

Decimal Notation

x = 0.3984375

Solution steps

lo g_{4} (2) - lo g_{4} (2 - 5 x) = 4

Move

lo g_{4} (2)

to the right side

- lo g_{4} (2 - 5 x) = 4 - lo g_{4} (2)

Divide both sides by

- 1

lo g_{4} (2 - 5 x) = - 4 + lo g_{4} (2)

Apply log rules

2 - 5 x = 4^{- 4 + \frac{1}{2}}

Solve

2 - 5 x = 4^{- 4 + \frac{1}{2}} : x = \frac{51}{128}

x = \frac{51}{128}

Verify Solutions:

x = \frac{51}{128}

True

The solution is

x = \frac{51}{128}

5 lo g_{3} (x) = - 3

y, x = 2 ln (y - 1)

lo g_{3} (x^{2} - x - 5) = 2

x, ln (\frac{15}{x}) = 0

1.023 = ln (\frac{0.01667}{a})

What is the answer to log_{4}(2)-log_{4}(2-5x)=4 ?
The answer to log_{4}(2)-log_{4}(2-5x)=4 is x= 51/128
Solve for x: log_{4}(2)-log_{4}(2-5x)=4
The solution is x= 51/128