What is the answer to ln(11.7-2.5x)=x-4 ?

The answer to ln(11.7-2.5x)=x-4 is x=-(2.5\W_{0}(\frac{e^{0.68})/(2.5))-11.7}{2.5}

Solve for x: ln(11.7-2.5x)=x-4

The solution is x=-(2.5\W_{0}(\frac{e^{0.68})/(2.5))-11.7}{2.5}

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ln (11.7 - 2.5 x) = x - 4

x = - \frac{2.5 W _{0} ( \frac{e ^{0.68}}{2.5} ) - 11.7}{2.5}

Decimal Notation

x = 4.19424 \dots

Solution steps

ln (11.7 - 2.5 x) = x - 4

f (x) = g (x),

then

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

e^{l n (11.7 - 2.5 x)} = e^{x - 4}

Simplify

e^{l n (11.7 - 2.5 x)} : 11.7 - 2.5 x

11.7 - 2.5 x = e^{x - 4}

Solve

11.7 - 2.5 x = e^{x - 4} : x = - \frac{2.5 W _{0} ( \frac{e ^{0.68}}{2.5} ) - 11.7}{2.5}

x = - \frac{2.5 W _{0} ( \frac{e ^{0.68}}{2.5} ) - 11.7}{2.5}

Verify Solutions:

x = - \frac{2.5 W _{0} ( \frac{e ^{0.68}}{2.5} ) - 11.7}{2.5}

True

The solution is

x = - \frac{2.5 W _{0} ( \frac{e ^{0.68}}{2.5} ) - 11.7}{2.5}

lo g_{4} (x + 7) = 3

2 lo g_{2} (4 x + 1) - 1 = 6

lo g_{6} (x + 27) - lo g_{6} (x - 8) = 2

lo g_{4} (x - 4) = 1 - lo g_{4} (x)

lo g_{3} (9 x) = 5 - lo g_{3} (8)

What is the answer to ln(11.7-2.5x)=x-4 ?
The answer to ln(11.7-2.5x)=x-4 is x=-(2.5\W_{0}(\frac{e^{0.68})/(2.5))-11.7}{2.5}
Solve for x: ln(11.7-2.5x)=x-4
The solution is x=-(2.5\W_{0}(\frac{e^{0.68})/(2.5))-11.7}{2.5}