What is the answer to 4x2-16x+13=3log_{2}(x) ?

The answer to 4x2-16x+13=3log_{2}(x) is x=(3\W_{0}((8ln(2)e^{\frac{13ln(2))/3})/(3))}{8ln(2)}

Solve for x: 4x2-16x+13=3log_{2}(x)

The solution is x=(3\W_{0}((8ln(2)e^{\frac{13ln(2))/3})/(3))}{8ln(2)}

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4 x 2 - 16 x + 13 = 3 lo g_{2} (x)

x = \frac{3 W _{0} ( \frac{8 l n ( 2 ) e ^{\frac{13 l n ( 2 )}{3}}}{3} )}{8 ln ( 2 )}

Solution steps

4 x \cdot 2 - 16 x + 13 = 3 lo g_{2} (x)

Switch sides

3 lo g_{2} (x) = 4 x \cdot 2 - 16 x + 13

Multiply the numbers:

4 \cdot 2 = 8

3 lo g_{2} (x) = 8 x - 16 x + 13

Add similar elements:

8 x - 16 x = - 8 x

3 lo g_{2} (x) = - 8 x + 13

Divide both sides by

3

lo g_{2} (x) = \frac{- 8 x + 13}{3}

f (x) = g (x),

then

a^{f (x)} = a^{g (x)}

2^{l o g_{2} (x)} = 2^{\frac{- 8 x + 13}{3}}

Simplify

2^{l o g_{2} (x)} : x

x = 2^{\frac{- 8 x + 13}{3}}

Solve

x = 2^{\frac{- 8 x + 13}{3}} : x = \frac{3 W _{0} ( \frac{8 l n ( 2 ) e ^{\frac{13 l n ( 2 )}{3}}}{3} )}{8 ln ( 2 )}

x = \frac{3 W _{0} ( \frac{8 l n ( 2 ) e ^{\frac{13 l n ( 2 )}{3}}}{3} )}{8 ln ( 2 )}

Verify Solutions:

x = \frac{3 W _{0} ( \frac{8 l n ( 2 ) e ^{\frac{13 l n ( 2 )}{3}}}{3} )}{8 ln ( 2 )}

True

The solution is

x = \frac{3 W _{0} ( \frac{8 l n ( 2 ) e ^{\frac{13 l n ( 2 )}{3}}}{3} )}{8 ln ( 2 )}

ln (a) = 10

lo g_{10} (a^{49}) = 2

lo g_{10} (x) + lo g_{10} (x + 8) = 2

lo g_{2} (\frac{40}{x}) = 3

lo g_{10} (x) = 2.10083394

What is the answer to 4x2-16x+13=3log_{2}(x) ?
The answer to 4x2-16x+13=3log_{2}(x) is x=(3\W_{0}((8ln(2)e^{\frac{13ln(2))/3})/(3))}{8ln(2)}
Solve for x: 4x2-16x+13=3log_{2}(x)
The solution is x=(3\W_{0}((8ln(2)e^{\frac{13ln(2))/3})/(3))}{8ln(2)}