Question

Complete the steps to evaluate the following expression, given log3a = −0. 631. Log3 a 3.

Answer 1

The completed steps to evaluate the given expression is $a = 3^{-0.631} \approx 0.5$

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

$a^b = c$

Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows

$b = log_a(c)$

Some properties of logarithm are:

$\log_a(b) = \log_a(c) \implies b = c\\\\\log_a(b) + \log_a(c) = \log_a(b \times c)\\\\\log_a(b) - \log_a(c) = \log_a(\frac{b}{c})\\\\\log_a(b^c) = c \times \log_a(b)\\\\\log_b(b) = 1\\\\\log_a(b) + \log_b(c) = \log_a(c)$

• Log with base e = 2.71828... is written as $\ln(x)$ simply.
• Log with base 10 is written as $\log(x)$ simply.

The considered equation is $\log_3(a) = -0.631$

$\log_3(a) = -0.631\\\\a = 3^{-0.631} \approx 0.5$ (from calculator).

Thus, the completed steps to evaluate the given expression is $a = 3^{-0.631} \approx 0.5$

Learn more about logarithm here:

brainly.com/question/20835449