To write the expression log₅4 - log₅6 in a single logarithm, we have to use change of base property and division property of logarithm.
Given that the expression is log₅4 - log₅6.
We are required to tell the name of the property of logarithm which will help us to express the expression in a single logarithm.
Change of base property is property which tells that [tex]log_{a}b=log_{x}b /log_{x}a[/tex].
Division of logarithm says that log(m/n)=log m-log n.
The expression is log₅4 - log₅6.
log₅4 - log₅6=log 4/log 5-log 6/log 5
=(log 4+log6)/log 5
=log(4*6)/log 5
=log 24/log 5
=log (24-5)
=log 19
Hence to write the expression log₅4 - log₅6 in a single logarithm, we have to use change of base property and division property of logarithm.
Learn more about change of base theorem at https://brainly.com/question/24788069
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