Express log^2A in terms of the logarithms of prime numbers

Tasjapr asked Jan 8, 2023

298,127 views

20 votes

Tasjapr asked Jan 8, 2023

2.9k points

Your comment on this question:

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Email me at this address if my answer is selected or commented on:Email me if my answer is selected or commented on

Privacy: Your email address will only be used for sending these notifications.

15 votes

Solution

$A=\frac{\sqrt[]{3}\sqrt[4]{125}}{7^3}$

And we want to find log_2 A and we can do this :

$\log _2A=(1)/(2)\log _2(3)+(3)/(4)\log _2(5)-3\log _2(7)$

And the reason is because:

$\log _2(\sqrt[4]{125})=\log _2(\sqrt[4]{25\cdot5})=\log _2(\sqrt[4]{5^3}))=(3)/(4)\log _2(5)$

Tomas Reimers answered Jan 14, 2023

3.1k points

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

1.6m questions

2.0m answers