Question

What is the solution to the equation log(2) x + log(2) 4 = 3 ?

Answer 1

A good start is knowing what \(\log _24 \) equals.

Answer 2

I know i have to re-write the equation but i don't know what to change it to to make it... addable.

Answer 3

Never worry about that. Can you tell me what \(\log_2 4\) is equal to?

Answer 4

You don't need a calculator to calculate \(\log_24\). What power of 2 is 4?

Answer 5

2

Answer 6

There you go. So \(\log_24 = 2\).
Now we have something like \(\log_2x + 2 = 3\).

Answer 7

Subtract 3 from both sides to start with.

Answer 8

\(\log_2x = 3 - 2\).

My mistake - subtract 2 from both sides.

Answer 9

so log(2) x=1
which means x is .10? or is that wrong?

Answer 10

\(\log_2x = 1\)

This just means that 2 to some power is 1.

Answer 11

What power of \(2\) is \(1\)?

Answer 12

Blah .5.

Answer 13

so x is equal to .5

Answer 14

How is \(2^{0.5} = 1?\)

Answer 15

careful

Answer 16

\[\Large \log_2 x = 1 \implies 2^1 = x\]

Answer 17

Hmm.

Answer 18

What lgbasallote said.

Answer 19

What is \(2^1\)?

Answer 20

oh man..long have i waited to say that \m/

Answer 21

I see.

Answer 22

isn't 2^1=2?

Answer 23

Yep

Answer 24

So that's it. \(x = 2\).

Answer 25

But then dosn't log(2)2+log(2)4 not equal 3? it would equal 4.

Answer 26

How so?

Answer 27

\( \color{Black}{\Rightarrow \log_22 = 1, \log 2_4 = 2 \Longrightarrow 2 + 1 = 3}\)

Answer 28

oh i see now! I'm a moron sorry! thank you for your help :)

Answer 29

Heh. You're welcome!