Advanced Math/Question

Advertisement


Question
Hello, thank you for taking my question. It is:

Assuming that x, y and a are positive numbers, use the properties of logarithms to write the following expression in terms of logarithms of x and y. The expression is:

log(a) 9th-sqrt(xy)

Answer
Hi Leo,
I hope you mean the logarithm (to base a) of the 9th root of xy (as opposed to the "9th square root").
So, the expression would become
log(a) (xy)^(1/9)
= log(a) [x^(1/9)].[y^(1/9)]
= log(a) [x^(1/9)] + log(a) [y^(1/9)]       (since log AB = log A + log B)
= [log(a) x]/9 + [log(a) y]/9
or just
(1/9)[log(a) x + log(a) y]

Regards

Advanced Math

All Answers


Answers by Expert:


Ask Experts

Volunteer


Ahmed Salami

Expertise

I can provide good answers to questions dealing in almost all of mathematics especially from A`Level downwards. I can as well help a good deal in Physics with most emphasis directed towards mechanics.

Experience

Aspiring theoretical physicist. I have been doing maths and physics all my life.

Education/Credentials
I teach mathematics and engineering physics.

©2016 About.com. All rights reserved.