Question

Which of the following is equivalent to the expression below ? log 3 -log 15

Answer 1

The equivalent expression to the logarithm of log 3 - log 15 can be $\mathbf{ log_{10} \ 5^{-1}}$ or $\mathbf{-log_{10}(5)}$ depending on the values given in your option.

Calculating logarithms without tables.

Logarithm without tables involves using the logarithm rules and not using the logarithm table to derive the logarithm values.

Given that:

• log (3) - log (15)

We can use the logarithm rules that say:

$\mathbf{log_a(x) - log_a(y) = log_a(\dfrac{x}{y})}$

$\mathbf{log_{10}(3) - log_{10}(15) = log_{10}(\dfrac{3}{15})}$

$\mathbf{= log_{10}(\dfrac{1}{5})}$
$\mathbf{= log_{10} \ 5^{-1}}$

=  $\mathbf{-log_{10}(5)}$

Therefore, we can conclude that the equivalent expression to the logarithm of log 3 - log 15 can be $\mathbf{ log_{10} \ 5^{-1}}$ or $\mathbf{-log_{10}(5)}$ depending on the values given in your option.

Learn more about calculating logarithms without tables here:

brainly.com/question/2499600

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