Question

What is the solution to the equation log 2 x - log 2 4 = 5 ?

Answer 1

what is
\[\log_{2} 4\]
?

Answer 2

well it's
\[\log_{2} 2^2=2\log_22\]

Answer 3

\[2\log_22=2*1=2\]

Answer 4

so you have \[\log_2x-2=5\] so
\[\log_2x=7\]

Answer 5

x = 2
x = 4
x = 32
x = 128

Answer 6

\[\log_ab=c \rightarrow b=a^c\]

Answer 7

try to write down these numbers in the form
\[2^n\]

Answer 8

for example

Answer 9

\[2^5=32\]

Answer 10

does it satisfy your equation?- no, because 5 is not equal to 7

Answer 11

try to write down 128 in that form, can you do that?

Answer 12

2^7

Answer 13

yes

Answer 14

log2x=7
does 2^7 satisfy this equation?

Answer 15

using this formula you can check that:
logab=c→b=a^c

Answer 16

Great thanks! :)

Answer 17

yw :)