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1:43 5:07 Suggested clip Properties of Logarithms Expressing as Sum and Difference of logs YouTubeStart of suggested client of suggested clip Properties of Logarithms Expressing as Sum and Difference of logs
A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
0:24 5:03 Suggested clip Sum of logarithms with same base | Logarithms | Algebra II | Khan YouTubeStart of suggested client of suggested clip Sum of logarithms with same base | Logarithms | Algebra II | Khan
The laws apply to logarithms of any base, but the same base must be used throughout a calculation. This law tells us how to add two logarithms together. Adding log A and log B results in the logarithm of the product of A and B, that is log AB. The same base, in this case 10, is used throughout the calculation.
4:04 5:07 Suggested clip Properties of Logarithms Expressing as Sum and Difference of logs YouTubeStart of suggested client of suggested clip Properties of Logarithms Expressing as Sum and Difference of logs
A useful property of logarithms states that the logarithm of a product of two quantities is the sum of the logarithms of the two factors. In symbols, logo(XY)=logo(x)+logo(y). (x y) = log b (x) + log b
combine + terms with multiplication. Cancel common factors. Combine — terms with division. Cancel common factors. Write as negative exponent. Use power rule.
What is the rule when you multiply two values with the same base together (x2 * x3)? 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 log of a product is the sum of the logs.
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