What is the answer to log_{2}(3x)=x-1 ?

The answer to log_{2}(3x)=x-1 is x=-(\W_{-1}(-(ln(2))/6))/(ln(2)),x=-(\W_{0}(-(ln(2))/6))/(ln(2))

Solve for x: log_{2}(3x)=x-1

The solution is x=-(\W_{-1}(-(ln(2))/6))/(ln(2)),x=-(\W_{0}(-(ln(2))/6))/(ln(2))

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lo g_{2} (3 x) = x - 1

x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

Decimal Notation

x = 4.86841 \dots, x = 0.19014 \dots

Solution steps

lo g_{2} (3 x) = x - 1

f (x) = g (x),

then

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

2^{l o g_{2} (3 x)} = 2^{x - 1}

Simplify

2^{l o g_{2} (3 x)} : 3 x

3 x = 2^{x - 1}

Solve

3 x = 2^{x - 1} : x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

Verify Solutions:

x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

True

, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

True

The solutions are

x = - \frac{W _{- 1} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}, x = - \frac{W _{0} ( - \frac{l n ( 2 )}{6} )}{ln ( 2 )}

5402 = - ln (1 - x)

x, 3 = lo g_{10} (x)

lo g_{x} (x + 20) = 2

lo g_{4} (x - 95) = lo g_{4} (x - 5) + 2

lo g_{10} (100 x) = 3

What is the answer to log_{2}(3x)=x-1 ?
The answer to log_{2}(3x)=x-1 is x=-(\W_{-1}(-(ln(2))/6))/(ln(2)),x=-(\W_{0}(-(ln(2))/6))/(ln(2))
Solve for x: log_{2}(3x)=x-1
The solution is x=-(\W_{-1}(-(ln(2))/6))/(ln(2)),x=-(\W_{0}(-(ln(2))/6))/(ln(2))