Inverse Relationship between Exponential & Log

Presentation

•

Mathematics

•

12th Grade

•

Practice Problem

•

Easy

•

CCSS

HSF-BF.B.4C, HSF-IF.C.7E, HSF-BF.B.4A

Standards-aligned

Charles Dillard

Used 3+ times

FREE Resource

5 Slides • 10 Questions

Today We Will...

Examine the inverse relationship between exponential and logarithmic functions.

Open Ended

What do you notice about the tables for each function?

Type response here

Open Ended

What do you notice about the points graphed for each function?

Type response here

Open Ended

How can we use our understanding of exponentials to help us graph logarithmic functions?

Type response here

Inverse Relationships

Let’s look at the inverse relationship between exponential & logarithmic functions for any base.

Desmos Illustration

Draw

Use the key features of f(x) = 2^x to identify the key features of f^-1(x) = log₂(x)

Draw

Use the key features of f(x) = 2^x to identify the key features of f^-1(x) = log₂(x)

Match

Match the inverse functions to each other.

$y=6^x$

$y=\frac{1}{3^x}$

$y=x^3$

$y=10^x$

$y=e^x$

$y=\log_6x$

$y=\log_{\frac{1}{3}}x$

$y=x^{\frac{1}{3}}$

$y=\log_{ }x$

$y=\ln x$

Logarithms are Exponents

The logarithm of a number is the exponent to which you must raise the given base to the produce the number.

This expression is read as “log base b of y”

Logarithms are Exponents

Consider these restrictions on the variables.

Reorder

Evaluate the following logarithmic expressions.

Place them in order from least to greatest.

$\log_5\left(\frac{1}{125}\right)$

$\log_44$

$\log_39$

$\log_216$

Draw

Frequently used Logarithms

Two frequently used logarithms are logarithms with base 10 and base e.

Multiple Select

Select all the logarithms the equal 3.

$\log_327$

$\log_336$

$\log_33$

$\log_5125$

$\log_{ }1000$

Reorder

Mentally evaluate the following logarithmic expressions.

Place them in order from least to greatest.

$\log\ \frac{1}{100}$

log 0.1

log 1

log 10

log 100

Complete Delta Math Expnentials and Logarithms

Today We Will...

Examine the inverse relationship between exponential and logarithmic functions.

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