What is the answer to log_{5}(2x+3)-log_{5}(x+1)=2 ?

The answer to log_{5}(2x+3)-log_{5}(x+1)=2 is x=-22/23

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log_{5}(2x+3)-log_{5}(x+1)=2

lo g_{5} (2 x + 3) - lo g_{5} (x + 1) = 2

x = - \frac{22}{23}

Decimal Notation

x = - 0.95652 \dots

Solution steps

lo g_{5} (2 x + 3) - lo g_{5} (x + 1) = 2

Add

lo g_{5} (x + 1)

to both sides

lo g_{5} (2 x + 3) - lo g_{5} (x + 1) + lo g_{5} (x + 1) = 2 + lo g_{5} (x + 1)

Simplify

lo g_{5} (2 x + 3) = 2 + lo g_{5} (x + 1)

Apply log rules

2 x + 3 = 25 (x + 1)

Solve

2 x + 3 = 25 (x + 1) : x = - \frac{22}{23}

x = - \frac{22}{23}

Verify Solutions:

x = - \frac{22}{23}

True

The solution is

x = - \frac{22}{23}

lo g_{10} (x) = 15

lo g_{10} (x) = - 9

lo g_{x} (50) = 4

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

x, lo g_{e} (x) = - 2

What is the answer to log_{5}(2x+3)-log_{5}(x+1)=2 ?
The answer to log_{5}(2x+3)-log_{5}(x+1)=2 is x=-22/23
Solve for x: log_{5}(2x+3)-log_{5}(x+1)=2
The solution is x=-22/23