"Express" something in terms of `X` and `Y` means to find an expression (formula, rule) that gives this "something" as a result of operations on `X` and `Y.` The example of a formula is `X+2Y.`
Denote the number in question `log_3(10)` as `Z.`
Then we need to "solve for Z", not "solve for X and Y".
To do this, we need some properties of logarithms:
`log_a(b*c) = log_a(b) + log_a(c),` (logarithm of a product)
`log_a(b/c) = log_a(b) - log_a(c),` (logarithm of a quotient)
`log_a(a) = 1,`
`log_b(a) = (log_c(a))/(log_c(b))` (change of a base),
`log_a(b) = 1/(log_b(a))` (a consequence of change of a base).
Then we can state that:
`log_3(10) = log_3(2*5) =` (log of a product)
`= log_3(2) + log_3(5) = log_3(6/3) + log_3(5)` (log of a quotient). Also I am rewriting 2 as `6/3` since `2 = 6/3`
`=log_3(6) - log_3(3) + log_3(5) =` (change of a base)
`= Y - 1 + (log_6(5))/(log_6(3)) = Y - 1 + X*log_3(6) =`
= Y - 1 + X*Y.
This is the expression we need.