Question

Solve 2 log 2x = 4. Round to the nearest thousandth if necessary. How do I solve this?

Answer 1

Convert this first into exponential function. Do you know how to do that?

Answer 2

No, I don't.

Answer 3

is it:

\[\Large 2\log_{2}x=4\]

or

\[\Large 2\log (2x)=4\]

??

Answer 4

\[2\log (2x)=4 \]

Answer 5

Always take note that \[\log_{a} b = c\] is also equal to \[a ^{c} = \]
So the convertion of it to exponential will be \[10^{4} = 2x ^{2}\]
Just tell me if you don't get it.

Answer 6

I don't understand. The possible answers are:
A) 50
B) 0.5
C) \[50\sqrt{2}\]
D) 2

Answer 7

There are a couple of ways to start this, but first off, you need to have an "isolated" log expression on the LHS, that is, not a coefficient of 2 in front of that log function.

since the right hand side is just a number, that's easy enough to deal with here by dividing both sides by 2:

\(\Large \dfrac{2\log(2x)}{2}=\dfrac{4}{2}\)
so:
\(\Large \log(2x)=2\)

Now, at this point it's really just a matter of understanding what the log function MEANS:

\(\Large \log_{b}x=y\) means exactly that \(\Large b^y=x\)

In other words, \(\Large \log_{b}x=y\) MEANS THAT y is the POWER to which you take the base 2, to get x.

So the exponential form and the log form are just two sides of the same coin: the output of the log is the exponent of the exponential; and the input of the log is the output (the result) of the exponential.

And, you also need to know that the notation: \(\Large \log a\) (with no "base" stated) means that you have a base of 10. In other words, \(\Large \log x=\log_{10}x\)

So can you use that to figure out what x is, in \(\Large \log(2x)=2\) ?

You should first convert it to the exponential form, simplify what you can, and you should have a simple little equation to solve for x. :)