Condense each expression to a single logarithm.: 8 log2 x + 2 log2 y
Use the properties:
`nlog_b a = log_b a^n`
`log_b a + log_b c = log_b(ac)`
Notice that terms should have the same bases (the small number beside log) to apply the properties.
Start with the use of the first property above:
n = 8, b = 2 and a = x
`8log_2 x = log_2 x^8`
Do the same with the second term.
n = 2, b = 2, and a = y
`2log_2 y = log_2 y^2`
So, you have `log_2x^8 + log_2y^2`
Then, use the second property.
b = 2, a = x^8 and c = y^2
`log_2x^8 + log_2y^2 = log_2(x^8 * y^2)`
Thus, the answer is `log_2 x^8y^2.`