Question

Consider the equation below. Log Subscript 4 Baseline (x 3) = log Subscript 2 Baseline (2 x) Which system of equations can represent the equation?.

Answer 1

Equal expressions can be taken equal to an another variable. The system of equations representing the equation is  $y = x + 3\\y = 4x + 8$

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

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

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 given equation is:

$\log_4(x+3) = \log_2(2 +x)$

Adding $\log_2(4)$ on both the sides, we get:

$\log_2(4) + \log_4(x+3) =\log_2(4) + \log_2(2 +x) \\\\log_2(x + 3) = log_2(4(2+x))\text{\: \: \: (using first and last property listed)}\\\\x+3 = 8+4x = y(say)$

The, we get two equations as:

$y = x + 3\\y = 4x + 8$

This is the needed system of equations.

Learn more about logarithms here:

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