What is the answer to log_{2}(x)=x-3 ?

The answer to log_{2}(x)=x-3 is x=-(\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(\W_{0}(-(ln(2))/8))/(ln(2))

Solve for x: log_{2}(x)=x-3

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

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

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

Decimal Notation

x = 5.44490 \dots, x = 0.13749 \dots

Solution steps

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

f (x) = g (x),

then

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

2^{l o g_{2} (x)} = 2^{x - 3}

Simplify

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

x = 2^{x - 3}

Solve

x = 2^{x - 3} : x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{8} )}{ln ( 2 )}

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

Verify Solutions:

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

True

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

True

The solutions are

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

lo g_{256} (x) = \frac{1}{4}

x, ln (y + 1) = ln (x - 1) + C

lo g_{5} (3 x^{2}) = lo g_{5} (27)

ln (x) = e^{7}

ln (3 x) - ln (4) = 2

What is the answer to log_{2}(x)=x-3 ?
The answer to log_{2}(x)=x-3 is x=-(\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(\W_{0}(-(ln(2))/8))/(ln(2))
Solve for x: log_{2}(x)=x-3
The solution is x=-(\W_{-1}(-(ln(2))/8))/(ln(2)),x=-(\W_{0}(-(ln(2))/8))/(ln(2))