Answer:
[tex]log_{b}(b^{x r}) [/tex]
Step-by-step explanation:
A picture of the question is shown in the figure attached. There we can see that the step corresponding to Properties of exponents is the option:
[tex]log_{b}(b^{x r}) [/tex]
which is equivalent to
[tex]log_{b}((b^{x})^{r}) [/tex]
This question is based on the property of exponents.Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].
Given that :
[tex]\bold{log_a(M^r)}[/tex]
In this question, we have choose appropriate correct option for for given expression.
According to the question,
It is given that,
[tex]\bold{log_a(M^r)}[/tex] ...(1)
Now, substitute the value of M = [tex]\bold{b^{x}}[/tex]. We get,
Thus, [tex]\bold{log_a(M^r)} = \bold{log _a((b^{x})^r)}[/tex] ...(2)
As we know that, by using the property of exponents,
[tex]\bold{(x^{m})^n = x ^{mn}}[/tex]
Now, applying this property in expression (2).
We get,
[tex]\bold{log _a((b^{x})^r)} = \bold{log _a(b^{x r})}[/tex]
Therefore, the correct option is (c), [tex]\bold{log _a(b^{x r})}[/tex].
For more details, prefer this link:
https://brainly.com/question/1807508
