Question

Which expression gives the quotient rule for logarithms?

Options

• \[\log_b\left(\frac{x}{y}\right)=\frac{\log_b x}{\log_b y}\]

• \[\log_b\left(\frac{x}{y}\right)=\log_b x-\log_b y\]

• \[\log_b\left(\frac{x}{y}\right)=\log_b x+\log_b y\]

• \[\log_b\left(\frac{x}{y}\right)=y\log_b x\]

Answer 1

The quotient rule changes division inside a logarithm into subtraction. Hence, \[\log_b\left(\frac{x}{y}\right)=\log_b x-\log_b y\].