What is the answer to ln(x^{0.5})=(ln(x))^{0.5} ?

The answer to ln(x^{0.5})=(ln(x))^{0.5} is x=e^4,x=1

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ln(x^{0.5})=(ln(x))^{0.5}

ln (x^{0.5}) = (ln (x))^{0.5}

x = e^{4}, x = 1

Decimal Notation

x = 54.59815 \dots, x = 1

Solution steps

ln (x^{0.5}) = (ln (x))^{0.5}

Apply log rules

0.5 ln (x) = ln^{0.5} (x)

Rewrite the equation with

ln (x) = u

0.5 u = u^{0.5}

Solve

0.5 u = u^{0.5} : u = 4, u = 0

u = 4, u = 0

Substitute back

u = ln (x),

solve for

x

Solve

ln (x) = 4 : x = e^{4}

Solve

ln (x) = 0 : x = 1

x = e^{4}, x = 1

Verify Solutions:

x = e^{4}

True

, x = 1

True

The solutions are

x = e^{4}, x = 1

ln (7 x + e) = 9

2.85 = - lo g_{10} (x)

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

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

lo g_{7} (2 x) + lo g_{7} (2) = 5

What is the answer to ln(x^{0.5})=(ln(x))^{0.5} ?
The answer to ln(x^{0.5})=(ln(x))^{0.5} is x=e^4,x=1
Solve for x: ln(x^{0.5})=(ln(x))^{0.5}
The solution is x=e^4,x=1