What are the steps I should use to solve this problem?
2 - 1/2 log(base)n 4 - log(base)n 5

Question

What are the steps I should use to solve this problem? 
2 - 1/2 log(base)n 4 - log(base)n 5

sighn0more · Answer

Would I need to convert the 2 to a log first?

anonymous · Answer

$$2-\log_{n} 4^{\frac{ 1 }{ 2 }}-\log_{n} 5=2-\log_{n} \left( 2*5 \right)$$

sighn0more · Answer

Don't the rules of logarithms state that when logs are subtracted they must be divided?

sighn0more · Answer

Also, the back of my math textbook writes that the answer to this problem is 1/2. The problem is that I do not know how to get to that answer.

misty1212 · Answer

HI!!

misty1212 · Answer

i do not see an equal sign there, so what exactly are you trying to "solve" 
maybe it means "combine as a single log"?

sighn0more · Answer

Hello! And it wants me to write the expression as either a single log or an integer

misty1212 · Answer

ok

misty1212 · Answer

that makes more sense

misty1212 · Answer

we can start with $$\frac{1}{2}\log(4)=\log(\sqrt4)=\log(2)$$

misty1212 · Answer

that since $$\frac{1}{2}\log(4)=\log(4^{\frac{1}{2}})$$

sighn0more · Answer

Okay, so we could re-write the problem as: 2 - logn2 - logn5 ?

misty1212 · Answer

then you have $$2-\log(2)-\log(5)$$

misty1212 · Answer

that is the same as $$2-(\log(2)+\log(5))$$

misty1212 · Answer

so $$2-\log(10)$$ after you multiply b

misty1212 · Answer

can't thing of any further to go, since you do not know the base

misty1212 · Answer

it is $$\log_n(10)$$ right? without knowing $n$ you cannot get a number out of this

sighn0more · Answer

Oh! I see. I forgot to distribute the negative sign. Hmmm.....yep! That seems to be right.

misty1212 · Answer

ok good
not $\frac{1}{2}$ for sure, unless you are told what exactly $n$ is equal to

sighn0more · Answer

Definitely! Sorry, that was an error on my part. I was looking at the wrong problem. Thank you!

misty1212 · Answer

$$\color\magenta\heartsuit$$