What is the answer to log_{3}(5x)=x ?

The answer to log_{3}(5x)=x is x=-(\W_{-1}(-(ln(3))/5))/(ln(3)),x=-(\W_{0}(-(ln(3))/5))/(ln(3))

Solve for x: log_{3}(5x)=x

The solution is x=-(\W_{-1}(-(ln(3))/5))/(ln(3)),x=-(\W_{0}(-(ln(3))/5))/(ln(3))

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lo g_{3} (5 x) = x

x = - \frac{W _{- 1} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}, x = - \frac{W _{0} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}

Decimal

x = 2.17027 \dots, x = 0.26866 \dots

Solution steps

lo g_{3} (5 x) = x

f (x) = g (x),

then

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

3^{l o g_{3} (5 x)} = 3^{x}

Simplify

3^{l o g_{3} (5 x)} : 5 x

5 x = 3^{x}

Solve

5 x = 3^{x} : x = - \frac{W _{- 1} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}, x = - \frac{W _{0} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}

x = - \frac{W _{- 1} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}, x = - \frac{W _{0} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}

Verify Solutions:

x = - \frac{W _{- 1} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}

True

, x = - \frac{W _{0} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}

True

The solutions are

x = - \frac{W _{- 1} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}, x = - \frac{W _{0} ( - \frac{l n ( 3 )}{5} )}{ln ( 3 )}

ln (x + 8) = 2

2 x ln (\frac{1}{x}) - x = 0

lo g_{10} (2 x - 6) = 2

lo g_{256} (x) = - \frac{3}{4}

x (2 ln (x) + 1) = 0

What is the answer to log_{3}(5x)=x ?
The answer to log_{3}(5x)=x is x=-(\W_{-1}(-(ln(3))/5))/(ln(3)),x=-(\W_{0}(-(ln(3))/5))/(ln(3))
Solve for x: log_{3}(5x)=x
The solution is x=-(\W_{-1}(-(ln(3))/5))/(ln(3)),x=-(\W_{0}(-(ln(3))/5))/(ln(3))