What is the answer to ln(x)-x*ln(0.05)=0 ?

The answer to ln(x)-x*ln(0.05)=0 is x=-(\W_{0}(-ln(0.05)))/(ln(0.05))

Solve for x: ln(x)-x*ln(0.05)=0

The solution is x=-(\W_{0}(-ln(0.05)))/(ln(0.05))

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ln (x) - x \cdot ln (0.05) = 0

x = - \frac{W _{0} ( - ln ( 0.05 ) )}{ln ( 0.05 )}

Decimal Notation

x = 0.35022 \dots

Solution steps

ln (x) - x ln (0.05) = 0

Move

x ln (0.05)

to the right side

ln (x) = x ln (0.05)

f (x) = g (x),

then

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

e^{l n (x)} = e^{x l n (0.05)}

Simplify

e^{l n (x)} : x

Simplify

e^{x l n (0.05)} : 0.0 5^{x}

x = 0.0 5^{x}

Solve

x = 0.0 5^{x} : x = - \frac{W _{0} ( - ln ( 0.05 ) )}{ln ( 0.05 )}

x = - \frac{W _{0} ( - ln ( 0.05 ) )}{ln ( 0.05 )}

Verify Solutions:

x = - \frac{W _{0} ( - ln ( 0.05 ) )}{ln ( 0.05 )}

True

The solution is

x = - \frac{W _{0} ( - ln ( 0.05 ) )}{ln ( 0.05 )}

y, ln (y) = ln (5 x) + c

2 ln (5) = ln (- 25 + c)

lo g_{7} (3 x + 1) - (2 x + 8) = 2

lo g_{10} (c + x^{2}) = 2 a

ln (16 x) - ln (4) = 2

What is the answer to ln(x)-x*ln(0.05)=0 ?
The answer to ln(x)-x*ln(0.05)=0 is x=-(\W_{0}(-ln(0.05)))/(ln(0.05))
Solve for x: ln(x)-x*ln(0.05)=0
The solution is x=-(\W_{0}(-ln(0.05)))/(ln(0.05))