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Exponential Form Express the equation in exponential form.$$\text { (a) } \log _{5}\left(\frac{1}{125}\right)=-3 \quad \text { (b) } \log _{8} 4=\frac{2}{3}$$

(a) \(5^{-3}=125\) (b) \(8^{\frac{2}{3}}=4\)

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 3

Logarithmic Functions

Functions

Campbell University

Harvey Mudd College

Idaho State University

Lectures

01:43

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. An example is the function that relates each real number x to its square x^2. The output of a function f corresponding to an input x is denoted by f(x).

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So remember that when we're converting from large, arrhythmic form of an equation to an exponential form of equation, Well, if we have Lord based B log base B of K is equal to X, we can convert this to exponential form by saying we have the base be to the exponents X, and this is equal to case. So let's do this for A and B So for a we have our basis five Our exponents is negative three and this gives us 1/1 25 for be. We have we have our bases for exponents are rather our bases. Eight, our bases eight, our exponents is 2/3 and this is equal to four. And so these are our solutions for A and B. We've converted from log rhythmic form to exponential for

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