Question

solve log 2x + log 12 =3 can someone please explain

Answer 1

write log 2x + log 12 as one log

log 2x*12=3

then apply base 10 exponential to both sides, which cancels the log on the left

2x*12=10^3

should be easy now

Answer 2

Do you know your laws of logarithms?

Answer 3

Well the left side can be combined into one log using the law that says

\[\log_{a}x+\log_{a}y=\log_{a}xy\]

Answer 4

Right, so that gives us

log 2x*12=3

when there is no base written it's the common log with base 10, to cancel a log out you apply that base exponential to both sides, in this case 10

2x*12=10^3

Answer 5

so 10^3 to both sides

Answer 6

No, base 10 exp. to both sides. Before i canceled the log out it would look like this

\[10^{\log 2x*12}=10^3\]

Answer 7

right, so the log and the 10 cancel, leaving you with

2x*12=10^3

Answer 8

Can you solve now?

Answer 9

You cant solve 24x=1000?

Answer 10

what happens to the x thats what confuses me

Answer 11

multiply 2*12 to get 24 and 10*10*10 to get 1000 then multiply the two together to get x which would be 24,000

Answer 12

x is what you're solving for...

2*12x=24x
10^3=1000

so, 24x=1000

just divide both sides by 24 and x is solved for

Answer 13

41.67

Answer 14

Yep

Answer 15

thank you for helping

Answer 16

No problem, if you get familiar with these laws of logarithms it makes these problems a lot easier

Answer 17

ok thanks