Question

Use the properties of logarithms to expand log6XEach logarithm should involve only one variable and should not have any exponents.Assume that all variables are positive.

Answer 1

Answer;

`\text{ log z - 6 log x}`

Explanation;

To solve this, we are going to use one of the logarithm rules

The rule is the subtraction and/or the division rule and it applies to logarithms having the same base

It can be summarized as;

`\log \text{ a - log b= log }(a)/(b)`

Looking at the question, we can see that we have an exponent; hence we shall be needing the exponent rule for logarithms here too. It can be represented as follows;

`^{}Loga^b\text{ = bLog a}`

So, we shall be applying these two rules to solve the problem at hand

`\begin{gathered} \log \text{ }(z)/(x^6) \\ =logz-logx^6 \\ =\text{ log z - 6 log x} \end{gathered}`