The equivalent expression to the logarithm of log 3 - log 15 can be [tex]\mathbf{ log_{10} \ 5^{-1}}[/tex] or [tex]\mathbf{-log_{10}(5)}[/tex] depending on the values given in your option.
Logarithm without tables involves using the logarithm rules and not using the logarithm table to derive the logarithm values.
Given that:
We can use the logarithm rules that say:
[tex]\mathbf{log_a(x) - log_a(y) = log_a(\dfrac{x}{y})}[/tex]
[tex]\mathbf{log_{10}(3) - log_{10}(15) = log_{10}(\dfrac{3}{15})}[/tex]
[tex]\mathbf{= log_{10}(\dfrac{1}{5})}[/tex]
[tex]\mathbf{= log_{10} \ 5^{-1}}[/tex]
= [tex]\mathbf{-log_{10}(5)}[/tex]
Therefore, we can conclude that the equivalent expression to the logarithm of log 3 - log 15 can be [tex]\mathbf{ log_{10} \ 5^{-1}}[/tex] or [tex]\mathbf{-log_{10}(5)}[/tex] depending on the values given in your option.
Learn more about calculating logarithms without tables here:
https://brainly.com/question/2499600
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