- #1
Paulo2014
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Homework Statement
Simplify fully: log a + log b – log b^2
The Attempt at a Solution
I don't even know where to start...
The "properties of logarithms" section of your textbook seems like the obvious place to start.Paulo2014 said:I don't even know where to start...
The simplified form of log a + log b – log b^2 is log(a/b).
No, log a + log b – log b^2 is already in its simplest form.
To simplify log a + log b – log b^2, you can use the logarithmic properties of addition and subtraction. First, you can combine the first two terms using the property log a + log b = log(ab). Then, you can use the property log b^2 = 2log b to rewrite the expression as log(ab) – 2log b. Finally, you can use the property log x – log y = log(x/y) to get the simplified form of log(a/b).
The base of the logarithm in log a + log b – log b^2 is not specified, so it can be any base. It is common to assume a base of 10, but it can also be written as ln(a/b) for a natural logarithm or log2(a/b) for a base 2 logarithm.
The simplified form of log a + log b – log b^2, which is log(a/b), can be used in calculations involving logarithms. For example, if you have an expression like log 10 + log 100 – log 10^2, you can simplify it to log(10/10) = log 1 = 0. This can be helpful in solving equations involving logarithms or in simplifying complex expressions.