### Concept (1)

In order to do problems on evaluating logarithms in terms of known quantities, we need to understand the rules of logarithms such as the product, the quotient and the power rules. When we say evaluating logarithms in terms of known quantities, we mean that we want to be able to rewrite a complex logarithm so that we can recognize certain simpler logarithmic terms within it.

### Sample Problems (5)

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Given log52 = j and log53 = k.

Express log56 in terms of j and k.
###### Problem 1
How to evaluate a logarithm as a product of logarithmic values in terms of variables.

Given log52 = j and log53 = k.

Express log5(4⁄9) in terms of j and k.
###### Problem 2
How to evaluate a logarithm as a composition (quotient and power) of known logarithmic values.

Given log52 = j and log53 = k.

Express log5(15⁄2) in terms of j and k.
###### Problem 3
How to evaluate a logarithm as a composition (product and quotient) of logarithmic values in terms of variables.
###### Problem 4
<p>How to use known logs to approximate other logs using the product rules, usually without a calculator.</p>
###### Problem 5
How to use known logs to approximate other logs using the quotient rule, usually without a calculator.