## Use the properties of logarithms to write the following expression as one logarithm.logslogr + 8logr s − 3logr t

### To simplify the expression logslogr + 8logr s – 3logr t, we can use the properties of logarithms, specifically the product rule and the power rule

To simplify the expression logslogr + 8logr s – 3logr t, we can use the properties of logarithms, specifically the product rule and the power rule.

The first term, logslogr, can be rewritten using the power rule as logr(slogr).

The second term, 8logr s, can be rewritten using the power rule as logr(s^8).

The third term, -3logr t, can be rewritten using the power rule as logr(t^(-3)).

Now, using the product rule, we can combine the terms with the same base, logr.

logr(slogr) + logr(s^8) – logr(t^(-3))

Using the product rule, we can combine the terms by adding the coefficients:

logr[(slogr)(s^8)(t^(-3))]

Simplifying further, we can use the power rule to rewrite the expression as:

logr[(s^(1+8))(t^(-3))]

logr(s^9)(t^(-3))

Finally, we can write the expression as one logarithm using the product rule:

logr[(s^9)/(t^3)]

Therefore, the expression logslogr + 8logr s – 3logr t can be written as one logarithm: logr[(s^9)/(t^3)].

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