This function is called the Natural Logarithm function and has the symbol ln. Solving Logarithmic Equations. All Rights Reserved.
Move the 2 and write as a power. Again, you have two exponential expressions that are equal to each other.
In this case, both sides have the same exponent, and this means the bases must be equal. Rewriting a logarithmic equation as an exponential equation is a useful strategy.
Remember, when no base is written, that means the base is 10. This first step in this problem is to get the logarithm by itself on one side of the equation with a coefficient of 1.
You can divide both sides of the equation by log 4 to get x by itself. Answer Use a calculator to evaluate the logarithms and the quotient.
If the two expressions are equal, then their exponents must be equal. Take the logarithm of both sides.
The first is one you have used before: When we write log x without a base, it is understood that the base is 10. Now, in this case it looks like the best logarithm to use is the common logarithm since left hand side has a base of 10.
Let's evaluate some logarithmic equations and expressions to practice our knowledge of properties of logs. However, we do need to be careful. Related Content. This point will always be the x intercept. Again, this property only works if the the base b is the same as the base b of the log.