Question

Use the properties of logarithms to write the expression as a single logarithm?

Answer 1

The logarithmic expression is log₆(x) + 4log₆(x) - log₆(x + 2).

Apply power property of logarithm : nlog_a(m) = log_a(m)ⁿ.

= log₆(x) + log₆(x⁴) - log₆(x + 2)

Apply product property of logarithm : log_a(m) + log_a(n) = log_a(mn)

= log₆(x * x⁴) - log₆(x + 2)

= log₆(x⁵) - log₆(x + 2)

Apply quotient property of logarithm : log_a(m) - log_a(n) = log_a(m/n).

= log₆[x⁵ / (x + 2)].

Therefore, the simplified expression is log₆[x⁵ / (x + 2)]