If the expression is log₃ 7(2 x-3)², then the expansion of the expression is [log 7+2 log (2x-3)]/ log 3.
Given that the expression is log₃ 7(2 x-3)².
We are told to find the expansion of the expression using change of base formula.
The change of base formula is basically used to re-write a logarithm operation as a fraction of logarithms with a new base.
It says that [tex]log_{a} b[/tex]= [tex]log_{x}b /log_{x}a[/tex].
The expression is log₃ 7(2 x-3)².
We know that log mn=log m +log n.
log₃ 7(2 x-3)²=[log 7+ log [tex](2x-3)^{2}[/tex]]/ log 3
We know that log [tex]a^{b}[/tex]=log b/log a.So,
=[log 7+2log (2x-3)]/log 3
Hence if the expression is log₃ 7(2 x-3)², then the expansion of the expression is [log 7+2 log (2x-3)]/ log 3.
Learn more about base change theorem at https://brainly.com/question/14998693
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