Index laws and the laws of logarithms are essential tools for simplifying and manipulating exponential and logarithmic functions. There is an inverse relationship between exponential and logarithmic ...

Exponential equations are mathematical expressions that involve exponentials, which have the form of a number raised to a power. These types of equations can appear challenging, but with the right ...

\({\log _a}a = 1\) (since \({a^1} = a\)) so \({\log _7}7 = 1\) \({\log _a}1 = 0\) (since \({a^0} = 1\)) so \({\log _{20}}1 = 0\) \({\log _a}p + {\log _a}q = {\log _a ...

In this section, you will: * Use like bases to solve exponential equations. * Use logarithms to solve exponential equations. * Use the definition of a logarithm to solve logarithmic equations. * Use ...

Exponential and logarithmic functions are mathematical concepts with wide-ranging applications. Exponential functions are commonly used to model phenomena such as population growth, the spread of ...

Before you get started, take this readiness quiz. Solve: x2=16. In the section on logarithmic functions, we solved some equations by rewriting the equation in exponential form. Now that we have the ...

The change of base formula serves as a useful tool when dealing with logarithms that have different bases. The formula is as follows: log_a (b) = log_c (b)/log_c (a), where ‘c’ is any base (typically ...