Question

plz check my answer
What is the solution to the equation log 2 x – log 2 4 = 2 ?
x = 1

x = 18

x = 8 --->My answer

x = 16

Answer 1

the problem is
\[ \log_2(x) - \log_2(4) = 2\]
use the property

\[ \log(a)- \log(b) = \log(a/b) \]
to combine the logs. can you do that ?

Answer 2

yes

Answer 3

you get
\[ \log_2\left(\frac{x}{4}\right) = 2\]

Answer 4

so it wou ld be 4x=2 then i get x=2 but that isnt one of the choices

Answer 5

you get
\[ \log_2\left(\frac{x}{4}\right) = 2 \]

to get rid of a log, make it the exponent of its *base*
make both sides have a base of 2:
\[ 2^{\log_2\left(\frac{x}{4}\right)}= 2^2\]

the mess on the left simplifies to x/4 (which is why we do this)
\[ \frac{x}{4}= 2^2\]
can you finish?

Answer 6

yes!!!
x/4=4
then i divide 4 by 4 and i get 1?

Answer 7

first step is ok
\[ \frac{x}{4} = 4\]

what is x ? if x is 1, you would get
\[ \frac{1}{4} = 4\] which is not correct. 1/4 does not equal 4
so x is not 1.

we could try x=2, and x=3 and so on, but there are an awful lot of numbers to check.

one way to find x is multiply both sides by 4
\[ 4\cdot \frac{x}{4} = 4 \cdot 4\]
on the left side, 4 "up top" and 4 "below" means 4/4 or 4 divided by 4, or just 1
you get
\[ x= 4 \cdot 4\]

Answer 8

oh ok i see thanks so much for helping me

Answer 9

See
http://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--thing-to-both-sides--two-step-equations
for a very short video on equations

Answer 10

thanks i will watch it