Question

assume \\(\log_{b}x = 0.24\\) and \\(\log_{b}y = 0.68\\). evaluate the following expression. \\(\log_{b}\frac{x}{y}\\) \\(\log_{b}\frac{x}{y}=\square\\) (type an integer or a decimal.)

Explanation:

Step1: Apply log quotient rule

The logarithm quotient rule states that $\log_b \frac{m}{n} = \log_b m - \log_b n$. So, for $\log_b \frac{x}{y}$, we can rewrite it as $\log_b x - \log_b y$.

Step2: Substitute given values

We know that $\log_b x = 0.24$ and $\log_b y = 0.68$. Substituting these values into the expression from Step 1, we get $0.24 - 0.68$.

Step3: Calculate the result

Performing the subtraction, $0.24 - 0.68 = -0.44$.

Answer:

-0.44