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

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

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

Answer

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))