Question

Given log Subscript 3 Baseline 2 almost-equals 0.631 and log Subscript 3 Baseline 7 almost-equals 1.771, what is log Subscript 3 Baseline 14?

Answer 1

Answer:

2.402

Step-by-step explanation:

I am going to write log subscript a baseline b as log_a(b)

Using the log rules we know one that says log_a(b*c) = log_a(b) + log_a(c)

We know log_3(2) and log_3(7).  What if we add them up?

log_3(2) + log_3(7)

Then using that log rule we get:

log_3(2) + log_3(7) = log_3(2*7) = log_3(14)

Since we know log of 2 and 7 individually we can just add them up.

log_3(14) = log_3(2) + log_3(7) = .631 + 1.771 = 2.402

Answer 2

The approximate value for given term is given by $log_3(14)= 2.402$

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

$b = \log_a(c)$

'a' is called base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

Some properties of logarithm are:

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

Using the log rules we know;

$log_a(bc) = log_a(b) + log_a(c)$

We have been given;

$log_3(2) + log_3(7)$

Then using that log rule we get:

$log_3(2) + log_3(7) = log_3(2\times 7) = log_3(14)$

$log_3(14) = log_3(2) + log_3(7) \\\\log_3(14)= .631 + 1.771 \\\\log_3(14)= 2.402$

Hence, The approximate value for given term is given by

$log_3(14)= 2.402$

Learn more about logarithm here:

brainly.com/question/20835449

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