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

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

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

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

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8 lo g_{2} (n) = n

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

Decimal Notation

n = 43.55926 \dots, n = 1.09999 \dots

Solution steps

8 lo g_{2} (n) = n

Divide both sides by

8

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

f (x) = g (x),

then

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

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

Simplify

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

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

Solve

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

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

Verify Solutions:

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

True

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

True

The solutions are

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

lo g_{10} (t) = - 6.016

lo g_{x} (16) = \frac{4}{5}

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

2 ln (x) - (ln (x))^{2} = 0

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

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