Expert Answers

An illustration of the letter 'A' in a speech bubbles

Given the equation e^(ln 2 + 3 ln x)

We need to simplify.

Let y= e^(ln 2 + 3lnx)

We know that a*lnb = ln b^a

Then we will rewrite 3ln x = ln x^3

==> y= e^(ln 2 + ln x^3)

Now, we know that ln a + ln b = ln a*b

Then, we will rewrite ln 2 + ln x^3 = ln 2x^3

==> y= e^(ln 2x^3)

Now, we know that e^ln x = x

==> y= 2x^3

Then we conclude that:

e^(ln 2 + 3lnx) = 2x^3

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

We have to simply e^ (ln 2 + 3 ln x)

Here we use the properties that d^ (a + b) = d^a * d^b

e^ (ln 2 + 3 ln x)

=> e^ (ln 2) * e^ (3 ln x)

a log b = log a^b

=> e^ (ln 2) * e^ (ln x^3)

Now for any logarithm to a base a x^ (log (x) b) = b

=> 2 * x^3

Therefore e^ (ln 2 + 3ln x) = 2*x^3

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial