Question

Condense the following logarithm: 5log_4(a) - 6log_4(b)​

Answer 1

Hi there! We are given the expression:

$\large \boxed{5 log_{4}(a) - 6 log_{4}(b) }$

To condense or simplify the following logarithm. You have to remember these properties:

Properties - Logarithm

$\large{ log_{b}(a)^{n} = n log_{b}(a) } \\ \large{ log_{b}(a) - log_{b}(c) = log_{b}( \frac{a}{c} ) }$

These two properties are what we need for our problem. Therefore,

$\large{ log_{4}(a)^{5} - log_{4}(b)^{6} }$

We use the log_b(a)^n = nlog_b(a) property to convert in the form above. Next, we use the second property.

$\large{ log_{4}( \frac{ {a}^{5} }{ {b}^{6} } ) }$

Answer

• log base 4 of (a^5/b^6) is our simplifed form.

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