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We have to solve for x given that ln x^3 = 2 + ln x

using the exponential rule for logarithms

ln x^3 = 2 + ln x

=> 3* ln x =2 + ln x

=> 3*ln x - ln x = 2

=> 2* ln x = 2

=> ln x = 1

As the base of ln is e x = e.

Therefore x = e.

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Given the logarithm equation:

ln x^3 = 2 + ln x

We need to fin x value that satisfies the equation.

First we will subtract ln x from both sides.

==> ln x^3 - ln x = 2

Now we will use the logarithm properties to solve.

We know that ln a - ln b = ln a/b

==> ln x^3 - ln x = ln x^3/x = ln x^2 = 2

==> ln x^2 = 2

Now we will rewrite using the exponent form.

==> x^2 = e^2

Since we have the powers are equal, then the bases are equal too.

==> x = e

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