Question

if \\(\log_{b}x = 0.38\\) and \\(\log_{b}z = 0.89\\), evaluate the following expression.\\(\log_{b}xz\\)\\(\log_{b}xz = \square\\)(type an integer or decimal.)

Explanation:

Step1: Recall logarithm product rule

The product rule for logarithms states that $\log_b(xy) = \log_b x + \log_b y$. So for $\log_b xz$, we can apply this rule.

Step2: Substitute given values

We know that $\log_b x = 0.38$ and $\log_b z = 0.89$. Using the product rule, $\log_b xz=\log_b x+\log_b z$. Substituting the values, we get $0.38 + 0.89$.

Step3: Calculate the sum

$0.38+0.89 = 1.27$.

Answer:

1.27