Question

Okay, I'm typing it hold on...

Answer 1

\[\log_{2} n= 1/4\log_{2} 16 + 1/2 \log_{2} 49\]

Answer 2

use the property
\[r\log(x)=\log(x^r)\] to rewrite
\[\frac{1}{4}\log_2(16)=\log_2(\sqrt[4]{16})=\log_2(2)\]

Answer 3

Use the property a log b (c) = log b (c)^a for each of the terms on the RHS..
and then use the property log a + logb = log(ab)

Answer 4

similarly
\[\frac{1}{2}\log_2(49)=\log_2(\sqrt{49})=\log_2(7)\]

Answer 5

this requires understanding that
\[\frac{1}{2}\log(49)=\log(49^{\frac{1}{2}})=\log(7)\]

Answer 6

Okay, I've written that on my paper... Could I make them all log 7s? Is that something Ican do

Answer 7

now on the right we have
\[\log_2(2)+\log_2(7)\] use the property
\[\log(N)+\log(M)=\log(MN)\] to write it as
\[\log_2(14)\]

Answer 8

oh

Answer 9

now you have finally
\[\log_2(n)=\log_2(14)\] which tells you \(n=14\)

Answer 10

we know that
\(\log_2(2)=1\) because \(2^1=2\) but that doesn't help us in this case, because we do not know what \(\log_2(7)\) is

Answer 11

because without a calculator we cannot solve \(2^y=7\) for \(y\)
but that is now what you need in this case, you just need the input is 14 on both sides

Answer 12

Okay, I think I understand that... I never really learned logs that well, and they've always been an issue. Thanks so much for your help. ^^