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

The answer to log_{4}(x+3)-log_{4}(x-5)=2 is x= 83/15

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

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

x = \frac{83}{15}

Decimal Notation

x = 5.53333 \dots

Solution steps

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

Add

lo g_{4} (x - 5)

to both sides

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

Simplify

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

Apply log rules

x + 3 = 16 (x - 5)

Solve

x + 3 = 16 (x - 5) : x = \frac{83}{15}

x = \frac{83}{15}

Verify Solutions:

x = \frac{83}{15}

True

The solution is

x = \frac{83}{15}

4 lo g_{10} (2 n) - 7 = - 11

lo g_{10} (x) = 5.6

lo g_{10} (x) = 5 - x

lo g_{6} (7 x) + 6 = 8

lo g_{8} (n) = 3

What is the answer to log_{4}(x+3)-log_{4}(x-5)=2 ?
The answer to log_{4}(x+3)-log_{4}(x-5)=2 is x= 83/15
Solve for x: log_{4}(x+3)-log_{4}(x-5)=2
The solution is x= 83/15