What is the answer to log_{4}(2+x)-log_{4}(3-5x)=3 ?

The answer to log_{4}(2+x)-log_{4}(3-5x)=3 is x= 190/321

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log_{4}(2+x)-log_{4}(3-5x)=3

lo g_{4} (2 + x) - lo g_{4} (3 - 5 x) = 3

x = \frac{190}{321}

Decimal Notation

x = 0.59190 \dots

Solution steps

lo g_{4} (2 + x) - lo g_{4} (3 - 5 x) = 3

Add

lo g_{4} (3 - 5 x)

to both sides

lo g_{4} (2 + x) - lo g_{4} (3 - 5 x) + lo g_{4} (3 - 5 x) = 3 + lo g_{4} (3 - 5 x)

Simplify

lo g_{4} (2 + x) = 3 + lo g_{4} (3 - 5 x)

Apply log rules

2 + x = 64 (3 - 5 x)

Solve

2 + x = 64 (3 - 5 x) : x = \frac{190}{321}

x = \frac{190}{321}

Verify Solutions:

x = \frac{190}{321}

True

The solution is

x = \frac{190}{321}

lo g_{4} (x) + 6 lo g_{x} (4) - 5 = 0

7.4 = 6.1 + lo g_{10} (x)

2 ln (x) = ln (x + 6)

lo g_{x} (x^{2} - 5 x - 4) = 1

ln (4 - c) = 0

What is the answer to log_{4}(2+x)-log_{4}(3-5x)=3 ?
The answer to log_{4}(2+x)-log_{4}(3-5x)=3 is x= 190/321
Solve for x: log_{4}(2+x)-log_{4}(3-5x)=3
The solution is x= 190/321