Can you subtract logarithms

Liza Sulkin. Logarithm addition and subtraction. Alex Federspiel. Video Properties of Logarithms by yaymath. Let's work through a problem together. Solve for x. Show Solution Check. This video by PatrickJMT covers addition and subtraction with logs of the same base. This video by ThinkwellVids video goes over some more complex logarithm examples. Simplify the following logarithmic expression:.

Possible Answers:. Correct answer:. Explanation : Each term can be simplified as follows: Combining these gives the answer:.

Report an Error. Simplify the expression using logarithmic identities. Explanation : The logarithm of a fraction is equal to the logarithm of the numerator minus the logarithm of the denominator. Use logarithmic properties to simplify this expression:. Expand the following logarithmic expression into a list of sums or subtractions of logarithms:. Explanation : One important property of logarithms is that multiplication inside the logarithm is the same thing as addition outside of it.

So our expression is the same as But also, exponents can be moved outside in the same way. Explanation : Remember the rules of logarithms: This means we can simplify it as follows: The logarithm of anything with the same base is always , so the correct answer is. Which of the following is another way to express? Explanation : Use the rule therefore. Which is another way of expressing? Explanation : Use the rule: therefore. Explanation : This problem can be solved using the properties of logs.

Explanation : In order to solve this problem you must understand the product property of logarithms and the power property of logarithms. Explanation : The rule for expanding and dividing logarithms is that you can subtract the terms inside the log. Copyright Notice. View Algebra 2 Tutors. Reza Certified Tutor. Irene Certified Tutor. University of Patras, Bachelor of Science, Mathematics. Sadrac Certified Tutor.

I prefer the natural log ln is only 2 letters while log is 3, plus there's the extra benefit that I know about from calculus. The base that you use doesn't matter, only that you use the same base for both the numerator and the denominator.

Remember that logarithms are exponents, so the properties of exponents are the properties of logarithms. The rule is that you keep the base and add the exponents. Well, remember that logarithms are exponents, and when you multiply, you're going to add the logarithms. The rule when you divide two values with the same base is to subtract the exponents.

Therefore, the rule for division is to subtract the logarithms.