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The expanded form of log [tex](ab)^{2}[/tex] using the laws of the logarithm is 2log a + 2log b.
The logarithm is the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if [tex]b^x[/tex] = n, which can be written as x = [tex]log_{b}[/tex] n.
For example, [tex]3^{2}[/tex] = 9; therefore, 2 is the logarithm of 9 to base 3, or [tex]2 =log_{3} 9[/tex]
Now, we will use the laws of the logarithm to expand the term log (ab)^2 as follows -
log [tex](ab)^{2}[/tex]
= 2 log (ab)
Using the product property, we will get,
= 2(log a + log b)
= 2log a + 2log b
Hence, the expanded form of log [tex](ab)^{2}[/tex] is 2log a + 2log b.
Read more about logarithms:
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The complete question is -
Use the laws of the logarithm to expand the term log (ab)^2.
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