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

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

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

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_{10} (x - 5) = 3

lo g_{5} (2 x + 1) + lo g_{5} (3) = 2

lo g_{7} (32) = 5 lo g_{7} (x)

ln (x) = 14.4247

lo g_{2} (x) - lo g_{2} (3 x) = 49

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