In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the 3 rd power: 1000 = 103 = 10 × 10 × 10.

The purpose of solving a logarithmic equation is to find the value of the unknown variable. In this article, we will learn how to solve the general two types of logarithmic equations, namely: Equations containing logarithms on one side of the equation. Equations with logarithms on opposite sides of the equal to sign.

If you see “log” without an explicit or written base, it is assumed to have a base of [latex]10[/latex]. In fact, a logarithm with base [latex]10[/latex] is known as the common logarithm. What we need is to condense or compress both sides of the equation into a single log expression.

The base b logarithm of a number is the exponent that we need to raise the base in order to get the number. The logarithm of the multiplication of x and y is the sum of logarithm of x and logarithm of y. The logarithm of the division of x and y is the difference of …

Sometimes a logarithm is written without a base, like this: log(100) This usually means that the base is really 10. It is called a "common logarithm". Engineers love to use it. On a calculator it is the "log" button. It is how many times we need to use 10 …

2022年11月16日 · In this section we will now take a look at solving logarithmic equations, or equations with logarithms in them. We will be looking at two specific types of equations here. In particular we will look at equations in which every term is a logarithm and we also look at equations in which all but one term in the equation is a logarithm and the term ...

Step 1: Use the rules of exponents to isolate a logarithmic expression (with the same base) on both sides of the equation. Step 2: Set the arguments equal to each other. Step 3: Solve the resulting equation. Step 4: Check your answers. Be sure to check to see if the solutions that you obtain solve the original logarithmic equation.

Solve a logarithmic equation algebraically. Solve a logarithmic equation graphically. Use the one-to-one property of logarithms to solve a logarithmic equation. Solve a radioactive decay problem.

In this explainer, we will learn how to solve logarithmic equations involving logarithms with different bases. Let’s first recall the relationship between logarithmic and exponential forms.

Using the Change-of-Base Formula, we can graph Logarithmic Functions with an arbitrary base. Example: Properties of Logarithms. 1. log MN = log M + log N. 2. log. 3. log. product rule. quotient rule. 5. log M = log N if and only if M = N . ) . Properties 1-3 may be used for Expanding and Condensing Logarithmic expressions.