What is the answer to ln(x)=3-2x ?

The answer to ln(x)=3-2x is x=(\W_{0}(2e^3))/2

Solve for x: ln(x)=3-2x

The solution is x=(\W_{0}(2e^3))/2

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ln (x) = 3 - 2 x

x = \frac{W _{0} ( 2 e ^{3} )}{2}

Decimal Notation

x = 1.34996 \dots

Solution steps

ln (x) = 3 - 2 x

f (x) = g (x),

then

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

e^{l n (x)} = e^{3 - 2 x}

Simplify

e^{l n (x)} : x

x = e^{3 - 2 x}

Solve

x = e^{3 - 2 x} : x = \frac{W _{0} ( 2 e ^{3} )}{2}

x = \frac{W _{0} ( 2 e ^{3} )}{2}

Verify Solutions:

x = \frac{W _{0} ( 2 e ^{3} )}{2}

True

The solution is

x = \frac{W _{0} ( 2 e ^{3} )}{2}

lo g_{a} (1 0^{1.8}) = 2.5752

85.6 = 10 \cdot lo g_{10} (W)

lo g_{10} (p) = - 2.6

ln (4 x) - 6 ln (x) = ln (2)

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

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