Question

log₃60-log₃10Write the expression as a single logarithm

Answer 1

When we subtract two logarithms with the same base, we can write it as a single logarithm:

$\log _ax-\log _ay=\log _a\frac{x}{y}$

In this problem, we have:

a = 3

x = 60

y = 10

Using those values in the above identity, we find:

$\begin{gathered} \log _360-\log _310=\log _3\frac{60}{10} \\ \\ =\log _36 \end{gathered}$

Therefore, the answer is:

$\log _36$