What is the answer to log_{4}(x+1)-log_{4}(5-4x)=1 ?

The answer to log_{4}(x+1)-log_{4}(5-4x)=1 is x= 19/17

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log_{4}(x+1)-log_{4}(5-4x)=1

lo g_{4} (x + 1) - lo g_{4} (5 - 4 x) = 1

x = \frac{19}{17}

Decimal Notation

x = 1.11764 \dots

Solution steps

lo g_{4} (x + 1) - lo g_{4} (5 - 4 x) = 1

Add

lo g_{4} (5 - 4 x)

to both sides

lo g_{4} (x + 1) - lo g_{4} (5 - 4 x) + lo g_{4} (5 - 4 x) = 1 + lo g_{4} (5 - 4 x)

Simplify

lo g_{4} (x + 1) = 1 + lo g_{4} (5 - 4 x)

Apply log rules

x + 1 = 4 (5 - 4 x)

Solve

x + 1 = 4 (5 - 4 x) : x = \frac{19}{17}

x = \frac{19}{17}

Verify Solutions:

x = \frac{19}{17}

True

The solution is

x = \frac{19}{17}

18 = 10 lo g_{10} (\frac{200}{x})

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

ln (3 x - 5) - 2 ln (x) = ln (2)

lo g_{3} (- 7 x + 1) - 7 = - 4

lo g_{3} (32) = 5 lo g_{3} (x)

What is the answer to log_{4}(x+1)-log_{4}(5-4x)=1 ?
The answer to log_{4}(x+1)-log_{4}(5-4x)=1 is x= 19/17
Solve for x: log_{4}(x+1)-log_{4}(5-4x)=1
The solution is x= 19/17