If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

Solve exponential equations using logarithms: base-10 and base-e

You might need: Calculator

Problem

Consider the equation 0, point, 3, dot, e, start superscript, 3, x, end superscript, equals, 27.
Solve the equation for x. Express the solution as a logarithm in base-e.
x, equals
Approximate the value of x. Round your answer to the nearest thousandth.
x, approximately equals
  • Your answer should be
  • an integer, like 6
  • an exact decimal, like 0, point, 75
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
Stuck?
Stuck?