Question

Which equation is equivalent to log subscript 3 baseline (x 5) = 2? 3 squared = left-bracket log subscript 3 baseline (x 5) right-bracket cubed 2 cubed = left-bracket log subscript 3 baseline (x 5) right-bracket squared 3 squared = x 5 2 cubed = x 5

Answer 1

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 $a^b = c$

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:

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

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

Log with base 10 is written as $\log(x)$ simply.

The equation given is:

$\log_3(x+5) = 2$

By using the definition of log, which says $a^b = c \leftrightarrow \log_a(c) = b$, we get:

$(x+5) = 2^3$ or $2^3 = x+5$

Thus, the equation that is equivalent to the considered equation of log is given by: Option E: $2^3 = x+5$

(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: $2^3 = x+5$

Learn more about logarithm here:

brainly.com/question/20835449