Hi there! We are given the expression:
[tex] \large \boxed{5 log_{4}(a) - 6 log_{4}(b) }[/tex]
To condense or simplify the following logarithm. You have to remember these properties:
Properties - Logarithm
[tex] \large{ log_{b}(a)^{n} = n log_{b}(a) } \\ \large{ log_{b}(a) - log_{b}(c) = log_{b}( \frac{a}{c} ) }[/tex]
These two properties are what we need for our problem. Therefore,
[tex] \large{ log_{4}(a)^{5} - log_{4}(b)^{6} }[/tex]
We use the log_b(a)^n = nlog_b(a) property to convert in the form above. Next, we use the second property.
[tex] \large{ log_{4}( \frac{ {a}^{5} }{ {b}^{6} } ) }[/tex]
Answer
- log base 4 of (a^5/b^6) is our simplifed form.
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