Write log_3 frac{1}{27x^{2} in the form a+b log_3x where a and b are integers

tricotasu 2021-02-25 Answered

Write log3127x2 in the form a+b log3x where a and b are integers

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Expert Answer

krolaniaN
Answered 2021-02-26 Author has 86 answers

Use the quotient property:
logb(mn)=logbmlogbn:
=log31log327x2
The logarithm of 1 (using any base) is 0:
=0log327x2
=log327x2
Use the product property: logbmn=logbm+logbn:
=(log327+log3x2)
=(log333+log3x2)
Use the rule: logbbx=x:
=(3+log3x2)
=3log3x2
Use the power property: logbxn=nlogbx
=32log3x

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