# Hotmath

Title:
Hotmath
Author:
Hotmath
Chapter: Exponential and Logarithmic Functions Section: Logarithmic Functions

Problem: 1

The expression log 3 243 means "the logarithm of with base ".

Problem: 3

Write the given equation in logarithmic form.

5 2 = 25.

Problem: 5

Write the given equation in logarithmic form.

.

Problem: 7

Write the given equation in logarithmic form.

Problem: 9

Write the given equation in logarithmic form.

.

Problem: 11

Determine the equivalent exponential form of the equation:

log 6 216 = 3

Problem: 13

Determine the equivalent exponential form of the equation:

Problem: 15

Write the given equation in exponential form.

log 6 1296 = 4.

Problem: 17

Evaluate the logarithm.

log 3 3 4 .

Problem: 19

Evaluate the logarithm.

log 4 64.

Problem: 21

Without using a calculator, evaluate the expression:

log 9 9

Problem: 23

log 3 243 = because to the power is 243.

Problem: 25

Without using a calculator, evaluate the expression:

log 3 81

Problem: 27

Find the value of the given expression:

Problem: 29

Without using a calculator, evaluate the expression:

Problem: 31

Without the help of a calculator, find log 3 243 and log 243 3.

Problem: 33

Simplify:

Problem: 35

Simplify:

Problem: 37

If g ( x ) = 7 x , then g –1 ( x ) = ? .

Give the domain and the range of g and g –1 .

Problem: 39

Find an equation for the inverse of the relation:

Problem: 41

Find an equation for the inverse of the relation:

y = ln 5 x

Problem: 43

Find an equation for the inverse of the relation:

y = ln ( x + 3)

Problem: 45

Given a logarithm function with equation y = log n x and the conditions n 0 and n 1, name one point which is on the graph of all such functions.

Problem: 47

Graph y = log 3 x and state the domain and range:

Problem: 49

Graph y = log ( x – 3) and state the domain and range.

Problem: 51

Graph

And state the domain and range.

Problem: 53

Solve the given equation.

log a 2 = 1 / 2

Problem: 55

Solve the given equation.

log 100 c = –0.5

Problem: 57

Solve the given equation.

log 11 x = 0

Problem: 59

Solve for x :

Problem: 61

Solve for x :

Problem: 63

Solve:

Problem: 65

Solve for x .

log 3 (3 x + 5) – log 3 ( x + 2) 3

Problem: 67

If 0 c 1 and 0 p 1, is log c p positive or negative?