4log b​ 3−log b​ 9

The expression you provided is "4log b​ 3−log b​ 9". To simplify this, we can use the properties of logarithms. Here are the steps:

1. Apply the power rule of logarithms, which states that log_b(a^n) = n*log_b(a), to the first term:

   4log_b(3) becomes log_b(3^4) = log_b(81)

2. The expression now is log_b(81) - log_b(9)

3. Now, apply the quotient rule of logarithms, which states that log_b(a) - log_b(c) = log_b(a/c):

   log_b(81) - log_b(9) becomes log_b(81/9)

4. Simplify 81/9 to get 9:

   log_b(81/9) becomes log_b(9)

So, "4log b​ 3−log b​ 9" simplifies to "log_b(9)".