Respuesta :
The equation that is equivalent to the considered equation of log is given by: Option E: 2^3 = x+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 [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]
'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:
[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) \times 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 equation given is:
[tex]\log_3(x+5) = 2[/tex]
By using the definition of log, which says [tex]a^b = c \leftrightarrow \log_a(c) = b[/tex], we get:
[tex](x+5) = 2^3[/tex] or [tex]2^3 = x+5[/tex]
Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]
(we used the fact that the question is asked in a way that expresses that there is only one equivalent equation. Plus we used the fact that as option E is a sure equivalent version, so it is correct option).
Thus, the equation that is equivalent to the considered equation of log is given by: Option E: [tex]2^3 = x+5[/tex]
Learn more about logarithm here:
https://brainly.com/question/20835449
