What is the answer to ln(x^2)+2=ln(x^4) ?

The answer to ln(x^2)+2=ln(x^4) is x=e,x=-e

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ln(x^2)+2=ln(x^4)

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

x = e, x = - e

Solution steps

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

Apply exponent rule:

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

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

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

Apply log rules

x^{2} = e^{2}

Solve

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

x = e, x = - e

Verify Solutions:

x = e

True

, x = - e

True

The solutions are

x = e, x = - e

lo g_{10} (4) + lo g_{10} (x + 4) = 1

lo g_{10} (x) (32) = \frac{1}{4}

2 lo g_{10} (x) = 6

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

ln (lo g_{2} (x)) = 1

What is the answer to ln(x^2)+2=ln(x^4) ?
The answer to ln(x^2)+2=ln(x^4) is x=e,x=-e
Solve for x: ln(x^2)+2=ln(x^4)
The solution is x=e,x=-e