Question

when writing the condensed log expression of $2\log_{5}(x) + 4\log_{8}(d)$, how many times would \log\ be written?

Explanation:

Step1: Apply power rule to logs

$2\log_{5}(x) = \log_{5}(x^2)$, $4\log_{8}(d) = \log_{8}(d^4)$

Step2: Check condensed form limits

The logs have different bases (5 and 8), so they cannot be combined into a single log expression.

Step3: Count "log" instances

The condensed form is $\log_{5}(x^2) + \log_{8}(d^4)$, which has 2 "log" terms.

Answer:

2