SOLUTION: How do I know that 1000^log 3 is (3)^3 and not (10^3)^log3?

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Question 1187990: How do I know that 1000^log 3 is (3)^3 and not (10^3)^log3?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


1000%5Elog%283%29=%2810%5E3%29%5Elog%283%29

So 1000^log3 IS equal to (10^3)^log3.

But "(10^3)^log3" is not a simplified form.

The objective is to find a simplified form of the given expression. So we do this:



And that IS a simplified form....

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

On logarithms and their properties,  see these introductory lessons
    - WHAT IS the logarithm
    - Properties of the logarithm
    - Change of Base Formula for logarithms
    - Evaluate logarithms without using a calculator
    - Simplifying expressions with logarithms
    - Solving logarithmic equations
in this site.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Logarithms".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.