What is the answer to 3+2log_{2}(x)=log_{2}(3-10x) ?

The answer to 3+2log_{2}(x)=log_{2}(3-10x) is x= 1/4

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3+2log_{2}(x)=log_{2}(3-10x)

3 + 2 lo g_{2} (x) = lo g_{2} (3 - 10 x)

x = \frac{1}{4}

Decimal Notation

x = 0.25

Solution steps

3 + 2 lo g_{2} (x) = lo g_{2} (3 - 10 x)

Apply log rules

8 x^{2} = 3 - 10 x

Solve

8 x^{2} = 3 - 10 x : x = \frac{1}{4}, x = - \frac{3}{2}

x = \frac{1}{4}, x = - \frac{3}{2}

Verify Solutions:

x = \frac{1}{4}

True

, x = - \frac{3}{2}

False

The solution is

x = \frac{1}{4}

lo g_{x} (243) = \frac{5}{6}

lo g_{x} (1000) = \frac{3}{2}

lo g_{10} (x^{2} - 1) = 2

4 lo g_{10} (3 - 2 x) = - 1

lo g_{2} (lo g_{2} (x)) = 4

What is the answer to 3+2log_{2}(x)=log_{2}(3-10x) ?
The answer to 3+2log_{2}(x)=log_{2}(3-10x) is x= 1/4
Solve for x: 3+2log_{2}(x)=log_{2}(3-10x)
The solution is x= 1/4