What is the answer to log_{5}(4x+7)-log_{5}(x)=2 ?

The answer to log_{5}(4x+7)-log_{5}(x)=2 is x= 1/3

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log_{5}(4x+7)-log_{5}(x)=2

lo g_{5} (4 x + 7) - lo g_{5} (x) = 2

x = \frac{1}{3}

Decimal Notation

x = 0.33333 \dots

Solution steps

lo g_{5} (4 x + 7) - lo g_{5} (x) = 2

Add

lo g_{5} (x)

to both sides

lo g_{5} (4 x + 7) - lo g_{5} (x) + lo g_{5} (x) = 2 + lo g_{5} (x)

Simplify

lo g_{5} (4 x + 7) = 2 + lo g_{5} (x)

Apply log rules

4 x + 7 = 25 x

Solve

4 x + 7 = 25 x : x = \frac{1}{3}

x = \frac{1}{3}

Verify Solutions:

x = \frac{1}{3}

True

The solution is

x = \frac{1}{3}

lo g_{10} (y) = (- 0.05085)

lo g_{2} ((r + 8)^{2}) = 4

8 lo g_{10} (n) - n = 0

ln (x - 10) = ln (8)

lo g_{x} (100) = 140

What is the answer to log_{5}(4x+7)-log_{5}(x)=2 ?
The answer to log_{5}(4x+7)-log_{5}(x)=2 is x= 1/3
Solve for x: log_{5}(4x+7)-log_{5}(x)=2
The solution is x= 1/3