What is the answer to x=8log_{2}(x) ?

The answer to x=8log_{2}(x) is x=-(8\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(8\W_{0}(-(ln(2))/8))/(ln(2))

Solve for x: x=8log_{2}(x)

The solution is x=-(8\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(8\W_{0}(-(ln(2))/8))/(ln(2))

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x = 8 lo g_{2} (x)

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Decimal Notation

x = 43.55926 \dots, x = 1.09999 \dots

Solution steps

x = 8 lo g_{2} (x)

Switch sides

8 lo g_{2} (x) = x

Divide both sides by

8

lo g_{2} (x) = \frac{x}{8}

f (x) = g (x),

then

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

2^{l o g_{2} (x)} = 2^{\frac{x}{8}}

Simplify

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

x = 2^{\frac{x}{8}}

Solve

x = 2^{\frac{x}{8}} : x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

Verify Solutions:

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

True

, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

True

The solutions are

x = - \frac{8 W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{8 W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

lo g_{2} (x) + 2 lo g_{4} (x - 1) - 1 = 0

27 = \frac{75}{ln ( x + 1 )}

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

lo g_{2 x - 3} (3 x^{2} - 18) = 2

4 ln (5 x - 4) - 11 = 5

What is the answer to x=8log_{2}(x) ?
The answer to x=8log_{2}(x) is x=-(8\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(8\W_{0}(-(ln(2))/8))/(ln(2))
Solve for x: x=8log_{2}(x)
The solution is x=-(8\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(8\W_{0}(-(ln(2))/8))/(ln(2))