Question

Find the exact value of the logarithm without using a calculator.
log2(8) + log2(16)

Answer 1

i know the answer, i want to know hwo to get to it

Answer 2

ansewr is 5

Answer 3

are these to the base 2 ?

Answer 4

yeah

Answer 5

use the properties of log, log(a) +log(b)=log(ab)
so using it here we get log(8)+log(16)=log(8*16) = log(\[2^{7}\]=7
loga(a) =1.

Answer 6

the answer is 7

Answer 7

no, the answer is 5.

Answer 8

oh my bad, different problem

Answer 9

\[log_2(8) + log_2(16) = log_2(2^3) + log_2(2^4) = 3 + 4 = 7\]

Answer 10

polpak keep doing it please

Answer 11

i like the way you doing it

Answer 12

Well brackett's method works better when you don't have exact powers of the base.

Answer 13

ok

Answer 14

but how you can figure out that 128=2^7?

Answer 15

Yeah, that's tough unless you know a lot of powers of 2.

Answer 16

\[\ln 128=\ln 2^x\]
\[\ln 128=x\ln2\]
\[\frac{\ln128}{\ln2}=x\]
\[x=\frac{\ln 2^7}{\ln2}=\frac{7*\ln2}{\ln2}=7\]