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

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

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

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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\frac{n}{lo g _{2} ( 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 )}

Solution steps

\frac{n}{lo g _{2} ( n )} = 8

Multiply both sides by

lo g_{2} (n)

n = 8 lo g_{2} (n)

Switch sides

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 )}

2 lo g_{6} (x - 7) + lo g_{6} (9) = 2

lo g_{8} (x) = 0.333

2 lo g_{3} (x) - lo g_{27} (x) = 10

lo g_{125} (x) = - \frac{1}{3}

y, ln (1 - 2 y) = - 2 t + c

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