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

The answer to log_{4}(5x+4)-log_{4}(4-x)=1 is x= 4/3

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

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

x = \frac{4}{3}

Solution steps

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

Add

lo g_{4} (4 - x)

to both sides

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

Simplify

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

Apply log rules

5 x + 4 = 4 (4 - x)

Solve

5 x + 4 = 4 (4 - x) : x = \frac{4}{3}

x = \frac{4}{3}

Verify Solutions:

x = \frac{4}{3}

True

The solution is

x = \frac{4}{3}

50 = 1200 \cdot lo g_{2} (x)

0.48 = lo g_{x} (x)

y, ln (y) = 3 ln (x)

lo g_{2} (lo g_{3} (x)) = 0

- 2 = lo g_{2} (x)

What is the answer to log_{4}(5x+4)-log_{4}(4-x)=1 ?
The answer to log_{4}(5x+4)-log_{4}(4-x)=1 is x= 4/3
Solve for x: log_{4}(5x+4)-log_{4}(4-x)=1
The solution is x= 4/3