prove: \$\\log_a \\left(\\frac{x}{y}\\right) = \\log_a x - \\log_a y\$.\nlet \$\\log_a x = m\$ and…

prove: \$\\log_a \\left(\\frac{x}{y}\\right) = \\log_a x - \\log_a y\$.\nlet \$\\log_a x = m\$ and \$\\log_a y = n\$. then by the definition of logarithms, \$x = \\square\$ and \$y = \\square\$.

Answer

Explanation:

Step1: Recall logarithm definition

The definition of a logarithm states that if $\log_{a}b = c$, then $b = a^{c}$.

Step2: Apply to $\log_{a}x = m$

Using the definition, for $\log_{a}x = m$, we have $x = a^{m}$.

Step3: Apply to $\log_{a}y = n$

Similarly, for $\log_{a}y = n$, we have $y = a^{n}$.

Answer:

$x = \boldsymbol{a^{m}}$ and $y = \boldsymbol{a^{n}}$