Question

Write the expression as a single logarithm. Identify any properties used.

3 log4 x + 2 log4 x

Answer 1

@freckles can you help me again

Answer 2

\[\text{ power rule } r \log_a(x)=\log_a(x^r) \\ \text{ product rule } \log_a(cd)=\log_a(c)+\log_a(d)\]

Answer 3

these are the two rules you will need

Answer 4

for the particular expression

Answer 5

so the first rule says you can do something with the 3 in front of log_4 (x)
and the 2 in front of log_4(x)

Answer 6

well there is another way to look at the problem
you do have like terms

Answer 7

So log4 x^3+ log4 x^2

Answer 8

cool

Answer 9

now use product rule

Answer 10

\[\log_a(c)+\log_a(d)=\log_a(c \cdot d)\]

Answer 11

log4(x^3*x^2) ?

Answer 12

cool

Answer 13

\[\log_4(x^3 \cdot x^2) \\ \log_4(x^{3+2})\]

Answer 14

Thats all I have to do?

Answer 15

well do 3+2 and then you are done

Answer 16

Ok. Thank you again lol

Answer 17

\[\log_4(x^5)\]

Answer 18

there is another way to have looked at this problem

Answer 19

you do have like terms above
3u+2u=5u
so you had
\[3\log_4(x)+2\log_4(x)=(3+2)\log_4(x)=5 \log_4(x) \\ \text{ which this should be fine as an answer too } \\ \text{ or using power rule you have } = \log_4(x^5) \\ \text{ either answer should be fine }\]

Answer 20

anyways be sure to mention the rules you used in your answer
because i see your teacher has that as instruction in this problem

Answer 21

Ok