The exponent of a number says how many times to use the number in a multiplication. In this example: 23 = 2 × 2 × 2 = 8.

In other words, logarithms are exponents. Remarks: log x always refers to log base 10, i.e., log x = log10x . ln x is called the natural logarithm and is used to represent logex , where the …

The following rules hold for any log c(x), c > 0, but are presented using the natural log function loge(x) = ln(x), as we will use this most often. Let a and b be real numbers.

When we need to expand a logarithm into multiple logarithms or compress multiple logarithms into a single logarithm, we use the logarithm rules. These rules are derived from the rules of …

These seven (7) log rules are useful in expanding logarithms, condensing logarithms, and solving logarithmic equations. In addition, since the inverse of a logarithmic function is an exponential …

The rules of logarithmic and exponential functions and the properties of these functions are presented. The use of these rules to simplify expressions and solve equations are explained …

Explain the relationship between exponential and logarithmic functions. Describe how to calculate a logarithm to a different base. Identify the hyperbolic functions, their graphs, and basic …

When the bases in an exponential equation cannot be made the same, taking the logarithm of each side is often the best way to solve it. For instance, in the equation 2 x = 3, there’s no …

We can use the power rule for logarithms to rewrite the log of a power as the product of the exponent and the log of its base. We can use the product rule, quotient rule, and power rule …

There is a good chance you have met logarithms. They turn multiplication into addition, which is a lot simpler. They are the basis for slide rules (not so important) and for graphs on log paper …