Question

How do I write the expression 4 logb x+ 6 logb q as a single logarithm ?

Answer 1

use these two properties:
1. \(\large log_bM + log_bN = log_b(MN) \)
2. \(\large log_b (M^N) = Nlog_bM\)

Answer 2

use #2 first then combine using #1 to make a single logarithm expression.

Answer 3

\[4\log _{b}x+6\log _{b}q=\log _{b }x ^{4}+\log _{b}q ^{6}=\log _{b}x ^{4}q ^{6}\]

Answer 4

Thank you both. Is there any way to check my answer on this sort of problem?

Answer 5

I don't see any way to go wrong with such a problem so don't worry much. Just remember your rules as mentioned above
\[Log a + Log b = Log ab\]
\[Log a - Log b = Log a/b\]
\[2Log a = Log a^2\]
\[Log_xy=2 --> x^2=y\]