What is the answer to ln(x^4)=6 ?

The answer to ln(x^4)=6 is x=esqrt(e),x=-esqrt(e)

Solve for x: ln(x^4)=6

The solution is x=esqrt(e),x=-esqrt(e)

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ln (x^{4}) = 6

x = e e, x = - e e

Decimal Notation

x = 4.48168 \dots, x = - 4.48168 \dots

Solution steps

ln (x^{4}) = 6

Apply exponent rule:

a^{2 \cdot n} = (a^{2})^{n}

x^{4} = (x^{2})^{2}

ln ((x^{2})^{2}) = 6

Apply log rules

x^{2} = e^{3}

Solve

x^{2} = e^{3} : x = e e, x = - e e

x = e e, x = - e e

Verify Solutions:

x = e e

True

, x = - e e

True

The solutions are

x = e e, x = - e e

2 lo g_{10} (x) = 4 lo g_{10} (3)

x, y = ln (x^{2} + y^{2})

lo g_{5} (x) + lo g_{5} (4 x - 1) = 1

ln (x) - ln (3) = 4

lo g_{2} (x) - lo g_{8} (x) = 4

What is the answer to ln(x^4)=6 ?
The answer to ln(x^4)=6 is x=esqrt(e),x=-esqrt(e)
Solve for x: ln(x^4)=6
The solution is x=esqrt(e),x=-esqrt(e)