Question

Which expressions are equivalent to the given expression?510810 I + 108,g 20 - 10810 10

Answer 1

Given the following properties for logarithms:

Then, from the problem, using (1):

`\begin{gathered} 5\log_(10)x+\log_(10)20-\log_(10)10 \\ \\ \log_(10)x^5+\log_(10)20-\log_(10)10 \end{gathered}`

Now, using (2):

`\log_(10)20\cdot x^5-\log_(10)10=\log_(10)(20x^5)-1`

Finally, using (3):

`\begin{gathered} \log_(10)(20x^5)/(10) \\ \\ \therefore\log_(10)(2x^5) \end{gathered}`

Answer: Third and last options