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

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

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

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

x = 5

Solution steps

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

Add

lo g_{5} (x)

to both sides

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

Simplify

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

Apply log rules

4 x + 5 = 5 x

Solve

4 x + 5 = 5 x : x = 5

x = 5

Verify Solutions:

x = 5

True

The solution is

x = 5

lo g_{10} (2 p) = 2 lo g_{10} (p)

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

lo g_{6} (4 x + 8) = 2

x, 0 = ln (x) + 5

x, lo g_{10} (x^{2}) = 2

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