Respuesta :
The completed steps to evaluate the given expression is [tex]a = 3^{-0.631} \approx 0.5[/tex]
What is logarithm and some of its useful properties?
When you raise a number with an exponent, there comes a result.
Lets say you get
[tex]a^b = c[/tex]
Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows
[tex]b = log_a(c)[/tex]
Some properties of logarithm are:
[tex]\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) + \log_b(c) = \log_a(c)[/tex]
- Log with base e = 2.71828... is written as [tex]\ln(x)[/tex] simply.
- Log with base 10 is written as [tex]\log(x)[/tex] simply.
The considered equation is [tex]\log_3(a) = -0.631[/tex]
[tex]\log_3(a) = -0.631\\\\a = 3^{-0.631} \approx 0.5[/tex] (from calculator).
Thus, the completed steps to evaluate the given expression is [tex]a = 3^{-0.631} \approx 0.5[/tex]
Learn more about logarithm here:
https://brainly.com/question/20835449
