Question

condense the expression to a single logarithm.

2log4 2+3log4 3

Answer 1

These are fun! ...

Answer 2

I can help...

Answer 3

yayy

Answer 4

That's\[2 \log _{4}(2)+3 \log _{4}(3)\]right?

Answer 5

There are two things with which you need be familiar in order to do these. One is the fact that when you see an addition sign between the two log terms, once upon a time they had been multiplied together. The other thing is that the 2 and the 3 out front once upon a time were exponents. So let's work backwards using those facts.

Answer 6

These rules are true as long as the log base is the same throughout the expression. Here the log base is 4 for both terms, so we are good.

Answer 7

okay then...

Answer 8

Let's deal with the exponents first. The 2 and the 3 out front had originally been exponents, so let's put them back where they came from like this:

Answer 9

\[\log _{4}(2)^{2}+\log _{4}(3)^{3}\]

Answer 10

Now we will deal with the addition thing, which originally had been a multiplication thing. So let's work backwards using that.

Answer 11

\[\log _{4}(2^{2}*3^{3})\]

Answer 12

That would simplify to

Answer 13

\[\log _{4}(4*9)\]

Answer 14

I mean 27, not 9. The 3 is cubed not squared.

Answer 15

\[\log _{4}(4*27)\]

Answer 16

ok

Answer 17

There's a lot more to logarithms than can be gone over in a forum such as this one. Rules can be shared and used in examples, but logs are not an easy concept to grasp, so it will take some practice. Those two concepts are two basic, sort of easy ones to learn.

Answer 18

so that's the answer.?

Answer 19

\[\log _{4}(4*27)\]

Answer 20

okay thank yhu so much your such a great help for me