A logarithmic equation can be solved using the properties of logarithms along with its inverse relationship with exponentials.
Properties of Logarithms:

 To solve most logarithmic equations:
1. Isolate the logarithmic expression
(you may need to use the properties of logarithms to create one logarithmic term).
2. Rewrite in exponential form (with a common base)
3. Use the inverse relationship with exponentials:
(where a > 0, a ≠1, and logax is defined).
4. Solve for the variable.
Things to remember

Remember that y = ex and
y = ln x are inverse functions.

Solve for x:
1.
 • Take e of both sides to eliminate the ln • Remember that ex and ln x are inverse function (one undoes the other).
2.
 • Isolate the log expression • Choose base 10 to correspond with log (base 10) • Apply composition of inverses and solve.
3.
 • Choose base 5 to correspond with the log base of 5.
4.
 • Isolate the ln expression first.
5.
 • You will need to use the log properties to express the two terms on the left as a single term. • Remember that log of a negative value is not a real number and is not considered a solution.
6.
7.
Using your graphing calculator, solve for x to the nearest hundredth.
Method 2: Place the left side of the equation into Y1 and the right side into Y2. Under the CALC menu, use #5 Intersect to find where the two graphs intersect.
Method 1: Rewrite so the equation equals 0.
Find the zeros of the function.
Both values are solutions, since both values allow for the ln of a positive value.