However when recalling something my algebra teacher had taught me during the year I came up with some questions regarding the logic recently. So I only have an Algebra II level understanding of math seeing as I am still in high school and am still missing some fundamentals seeing as I didn't pay attention in math until this year. Zero/Zero questions and perhaps faulty logic = log 5 [ ( x − 2 ) ( x − 6 ) Not exactly what you’re looking for? To simplify the quantity inside the parenthesis of log 5, cancel out the common x−6 factor. ⋆ The expression x 2 − 8 x + 12 can be written as ( x − 6 ) ( x − 2 ).
In this problem a = 5, m = x 2 − 8 x + 12 and n = ( x − 6 ) 2
⋆According to the quotient property of logarithm, the logarithm of the quotient of two numbers is equal to the difference of their individual logarithms, that is, log a ( m ) − log a ( n ) = log a ( m n ). Use power property to express 2 log 5 ( x − 6 ) as log 5 ( x − 6 ) 2 ⋆According to the power property of logarithm, the logarithm of the exponent of a number ( p q ) is equal to the exponent times the logarithm of the number (p), that is, q log a ( p ) = log a ( p q ). To express log 5 ( x 2 − 8 x + 12 ) − 2 log 5 ( x − 6 ) as a single logarithm consider the following steps. Similarly if the base of the logarithm is e, then it is called natural logarithm, examples log e ( y ), log e ( 102.25 ) etc. If the base of the logarithm is 10, then it is called the common logarithm, example log 10 ( y ), log 10 ( 102 ) etc. According to the base changing rule, logarithm of any number to the base a can be converted into another, that is log a ( y ) = log b ( y ) log b ( a ) According to the definition of logarithm, if y = a x, then log a ( y ) = x, where a is called the base of the logarithm.
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