Question

rewrite the logarithmic expression as a single logarithm with the same base\
\\(\log 5 + \log 2 + \log 9\\)

Explanation:

Step1: Recall log addition rule

The product rule of logarithms states that \(\log_a M + \log_a N=\log_a(M\times N)\) for the same base \(a\). We start with \(\log 5+\log 2+\log 9\). First, combine \(\log 5\) and \(\log 2\).
Using the rule, \(\log 5+\log 2=\log(5\times2)=\log(10)\)

Step2: Combine with the next log

Now we have \(\log(10)+\log 9\). Apply the product rule again.
\(\log(10)+\log 9=\log(10\times9)=\log(90)\)

Answer:

\(\log(90)\)