What is the answer to ln(1/x)+ln(2x^3)=ln^3(x) ?

The answer to ln(1/x)+ln(2x^3)=ln^3(x) is x=0.68908…,x=0.30399…,x=4.77382…

Solve for x: ln(1/x)+ln(2x^3)=ln^3(x)

The solution is x=0.68908…,x=0.30399…,x=4.77382…

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ln (\frac{1}{x}) + ln (2 x^{3}) = ln^{3} (x)

x = 0.68908 \dots, x = 0.30399 \dots, x = 4.77382 \dots

Solution steps

ln (\frac{1}{x}) + ln (2 x^{3}) = ln^{3} (x)

Apply log rules

- ln (x) + ln (2) + 3 ln (x) = ln^{3} (x)

Rewrite the equation with

ln (x) = u

- u + ln (2) + 3 u = u^{3}

Solve

- u + ln (2) + 3 u = u^{3} : u \approx - 0.37239 \dots, u \approx - 1.19075 \dots, u \approx 1.56314 \dots

u \approx - 0.37239 \dots, u \approx - 1.19075 \dots, u \approx 1.56314 \dots

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = - 0.37239 \dots : x = 0.68908 \dots

Solve

ln (x) = - 1.19075 \dots : x = 0.30399 \dots

Solve

ln (x) = 1.56314 \dots : x = 4.77382 \dots

x = 0.68908 \dots, x = 0.30399 \dots, x = 4.77382 \dots

Verify Solutions:

x = 0.68908 \dots

True

, x = 0.30399 \dots

True

, x = 4.77382 \dots

True

The solutions are

x = 0.68908 \dots, x = 0.30399 \dots, x = 4.77382 \dots

2 lo g_{10} (x) + 1 = lo g_{250} (x)

lo g_{10} (x) - 4 (\frac{1 - x}{2}) = 1

ln (2 x + 1) - ln (x - 6) = 0

lo g_{10} (x) = 5

lo g_{2} (2 x + 7) = 4

What is the answer to ln(1/x)+ln(2x^3)=ln^3(x) ?
The answer to ln(1/x)+ln(2x^3)=ln^3(x) is x=0.68908…,x=0.30399…,x=4.77382…
Solve for x: ln(1/x)+ln(2x^3)=ln^3(x)
The solution is x=0.68908…,x=0.30399…,x=4.77382…