solve the follwing:  ln e^3 + ln x^2 = ln (e^5)*x

Expert Answers

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

ln e^3 + ln x^2 = ln *e^5*x

We know that:

ln a^b = b ln a

==> 3ln e + 2ln x = ln (e^5)*x

Also, we know that ln x+ ln y = ln x*y

==> 3ln e + 2 ln x = ln e^5 + ln x

==> 3ln e + 2 ln x = 5 ln e + ln x

But ln e = 1

==> 3 + 2ln x = 5 + ln x

Now let us group similars:

==> ln x = 2

==> x = e^2

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