how to solve exponential equations

How to Solve Exponential Equation Like Your Professor

Several exponential equations can not resolve easily; there is no method to change the bases into the similar, like the resolution of 9 and 27 to the powers of 3. In answering these complex equations, learners need to practice logarithms. That is why learning the methods for how to solve exponential equation becomes necessary.

Practicing logarithms can enable the users to get the logarithm norms’ benefits that state that the powers within the log could be driven in the beginning as multipliers. With the exponential log, the learners can later transfer the different variables (as in the exponent, which is now within a log) in appearance as a multiplier at the log terms. The logarithm rule lets the leaners to relocate the variable behind over the ground, wherever a leaner could get their grips on it.

In this post, we will help you with the solution of how to solve exponential equation with the help of a logarithm. In addition to this, we will provide examples that will help the learners understand its concept. So, let’s move to the steps to solve these exponential equations.

Assignment help

Procedure for how to solve exponential equation with the help of logarithms

  1. Put the exponential equations on the one side and other numeric terms on the other side of the equation.
  1. Now, take the log on each side of the equations. The leaners can also use the bases of the logarithms.
  1. Get the solution of each variable. Take the answer in the round off decimal value or with the exact number. Moreover, remember to check the basic log rules to help the learners solve in one or another way.
Some basic rules for the logarithm
Log (a^x) = x. Log (a)Log base b (1) = 0Log base a (a) = 1Ln (e^a) = aLn (1) = 0Ln (e) = 1

Check the example for how to solve exponential equation

Problem: Get the solution for exponential equation 5^x = 15.

The exponential expression’s excellent information is that it is already separated on the left-hand side. Learners can instantly practice the log of each equations’ sides. It does not signify what base of the logarithmic can be utilized. The last statement must get out the equivalent. The most suitable option for the base of the log method is 5 because it is the exponential equation’s base itself. However, learners can also practice in the measurement of base 10, and the natural base must be e to prove that these all will have identical results in the end.

  • Log base of 5:

5^x = 15

Log base 5 (5x) = log base of 5 (15)

x. log base 5 (5) = log base of 5 (15)

x.(1) = log base of 5 (15)

X = [log (15)] / log (5)]

X = 1.6826 

X = 1.7 (approx)

  • Log base of 10

5^x = 15

Log base 10 (5x) = log base of 10 (15)

x. log base 10 (5) = log base of 10 (15)

X = log base of 10 (15) / log base of 10 (5)

X = [log (15)] / log (5)]

X = 1.7 (approx)

  • Log base of natural e

5^x = 15

ln (5x) = ln (15)

x. ln (5) = ln (15)

x = ln (15) / ln (5)

X = 1.6826 

X = 1.7 (approx)

Problem: Get the solution for exponential equation 11[10^(x-6)] = 121.

This is another example of how to solve exponential equation. As one can understand, the exponential equation on the left-hand side is not simplified itself. Learners need to eliminate the term 11 that is multiplied with the exponential equation. To do it, divide each side with 11. That will leave the expression just as an exponential equation on the left side and 11 on the other side after simplifying.

[11 (10^(x-6)]/ 11 = 121

10^(x-6) = 11

This is the right time to use the log on each side. Because the exponential equation has base 10, which is a suitable base to do the logarithm operation. Besides this, one can also answer this utilizing the natural base e to analyze if your last results match or not.

  • Log base of 10:

10^(x-6) = 11

Log base 10 (10 ^(x-6)) = log base of 10 (11)

(x-6). log base 10 (10) = log base of 10 (11)

(X-6) = log base of 10 (11) / log base of 10 (10)

X = [log (11)] / 1] + 6

X = 7.04 (approx)

  • Log base of natural e

10^(x-6) = 11

(x – 6) ln (10) = ln (11)

(x-6). ln (10) = ln (11)

x-6 = ln (11) / ln (10)

X = 1.04 +6 

X = 7.04 (approx)

Here, we have seen that both examples have the same result using the log (5), log (0), and that of natural log (ln). This is a method for how to solve exponential equation in an easy way.


To sum up this post, we can say that we have defined the possible methods about how to solve exponential equation. Moreover, we have mentioned the procedure for solving the exponential equations that help students solve mathematics in their daily lives. Besides this, we have provided solutions with detailed examples.

So that students can easily understand the techniques and implement them to solve exponential terms. Analyzing these examples can allow the students to know the sequence of solving an exponential equation. Follow the steps as mentioned above to get the desired result of the exponential and verify it accordingly. Learn and practice the initial rule table to solve each problem of exponential effectively. Get the best help in math homework.

Leave a Comment

Your email address will not be published.

This site uses Akismet to reduce spam. Learn how your comment data is processed.