Question: Show that log a b = 1/log b a, where a and b are positive real numbers, a 1, and b 1.

Show that loga b = 1/logb a, where a and b are positive real numbers, a ≠ 1, and b ≠ 1.

Step by Step Solution

★★★★★

3.26 Rating (158 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

To prove the equation logb 1 logb where logb represents the logarithm of b to the base a well use th... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Q:

Consider the function f(x) = (ab x + (1 - a)c x ) 1/x , where a, b, and c are positive real numbers with 0

Q:

Show that log a m = log a m 2 , where a and m are positive real numbers and a 1.

Q:

Show that log a (1/N) = log a N, where a and N are positive real numbers and a 1.

Q:

\fsh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m Math 280 Strategies of Proof Fall 2007 Class Notes 3.6 Proving Conditional Statements II: Indirect Proofs In Section 3.4, we studied...

Q:

University of Maryland University College Math 107 - College Algebra Quiz 5 Free Response, Multiple Choice, and Yes/No Problems, 6 Points Each. You may write answers after problems (you may use...

Q:

QUIZ: QUIZ TO This question: 22 Submit quiz point(s) possible Use the properties of logarithms to write the expression as a sum, difference, or product of simpler logarithms. For example, log 2...

Q:

Answer 6.1, 6.3, 6.4, 6.6, 6.9, 6.14, 6.15, 8.1, 8.5, 8.8, 8.13, and 8.19 Problem 6.1 Show that there exist integers m and n such that 3m + 4n = 25. Problem 6.2 Show that there is a positive integer...

Q:

In Java (keep numbers as fractions dont convert to doubles) Objectives Familiarity with using while loops and static methods Exposure to using nested while and for loops and arrays The Problem In his...

Q:

Objectives Familiarity with using while loops and static methods Exposure to using nested while and for loops and arrays The Problem In his book Irreligion , the mathematician John Allen Paulos tells...

Q:

Fall Session II 2021/MAT 100/E1 / Assignment 1 / Assignment1 Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a #1 and b #1. 3...

Q:

Being a pet lover, you always look for the best dogfood, toys and accessories for your beloved dogs and cats. You have noticed that in your neighborhood, there are no nearby pet shops that can cater...

Q:

Broadcast television commercials and magazine print ads are considered types of _________________ advertising media channels. Group of answer choices unconventional miscellaneous interactive...