What is the answer to n-8*log_{2}(n)=0 ?

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

Solve for n: n-8*log_{2}(n)=0

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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n - 8 \cdot lo g_{2} (n) = 0

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

n - 8 lo g_{2} (n) = 0

Move

n

to the right side

- 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 )}

ln (x) = e^{l n (3)}

20 lo g_{10} (x) = 50 \cdot 33.1

5 = lo g_{2} (n)

ln (x) = ln (x + 7) - ln (2)

f (n) = lo g_{2} (n), g (n) = n

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