AA Logarithmic Equations

The product rule states that $$\log_b(mn) = \log_b(m) + \log_b(n)$$ for any positive numbers m and n.

The quotient rule states that $$\log_b\left(\frac{m}{n}\right) = \log_b(m) - \log_b(n)$$ for any positive numbers m and n.

The power rule states that $$\log_b(m^k) = k \cdot \log_b(m)$$ for any positive number m and any real number k.

Using the product and quotient rules, it expands to $$2\log_b(x) + \log_b(y) - 3\log_b(z)$$ .

It condenses to $$\log_2\left(\frac{x^3y^2}{z^4}\right)$$ .

The change of base formula states that $$\log_b(a) = \frac{\log_k(a)}{\log_k(b)}$$ for any positive k.

It can be rewritten as $$\frac{\log(75)}{\log(5)}$$ .

It can be rewritten as $$\frac{\log(64)}{\log(3)}$$ .

A logarithm is the exponent to which a base must be raised to produce a given number, expressed as $$\log_b(a) = c$$ if and only if $$b^c = a$$ .

The base of a logarithm is the number that is raised to a power to obtain a certain value, denoted as b in $$\log_b(a)$$ .