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

The answer to log_{5}((2x+3)^2)-log_{5}(x)=2 is x= 9/4 ,x=1

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

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

x = \frac{9}{4}, x = 1

Decimal Notation

x = 2.25, x = 1

Solution steps

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

Add

lo g_{5} (x)

to both sides

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

Simplify

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

Apply log rules

(2 x + 3)^{2} = 25 x

Solve

(2 x + 3)^{2} = 25 x : x = \frac{9}{4}, x = 1

x = \frac{9}{4}, x = 1

Verify Solutions:

x = \frac{9}{4}

True

, x = 1

True

The solutions are

x = \frac{9}{4}, x = 1

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

lo g_{10} (x) = 1 - lo g_{10} (x - 3)

ln (x) + ln (x - 4) = ln (4)

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

lo g_{7} (x^{2} - 9) = 1

What is the answer to log_{5}((2x+3)^2)-log_{5}(x)=2 ?
The answer to log_{5}((2x+3)^2)-log_{5}(x)=2 is x= 9/4 ,x=1
Solve for x: log_{5}((2x+3)^2)-log_{5}(x)=2
The solution is x= 9/4 ,x=1