What is the answer to e^xln(x)-ln(x^2)=0 ?

The answer to e^xln(x)-ln(x^2)=0 is x=1,x=ln(2)

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e^xln(x)-ln(x^2)=0

e^{x} ln (x) - ln (x^{2}) = 0

x = 1, x = ln (2)

Decimal Notation

x = 1, x = 0.69314 \dots

Solution steps

e^{x} ln (x) - ln (x^{2}) = 0

Apply log rules

ln (x) (e^{x} - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

ln (x) = 0 or e^{x} - 2 = 0

Solve

ln (x) = 0 : x = 1

Solve

e^{x} - 2 = 0 : x = ln (2)

Verify Solutions:

x = 1

True

, x = ln (2)

True

The solutions are

x = 1, x = ln (2)

lo g_{10} (X) = 2

ln (x^{2} - 2 x) = 1

x, lo g_{10} (y) = ln (x)

lo g_{10} (n) = 6

lo g_{10} (n) = 1

What is the answer to e^xln(x)-ln(x^2)=0 ?
The answer to e^xln(x)-ln(x^2)=0 is x=1,x=ln(2)