how do i solve
4^(3x)=12

Question

how do i solve
4^(3x)=12

saifoo.khan · Answer

$$\huge 3x = \log_4 12$$

anonymous · Answer

so how do i solve, Is that the answer

saifoo.khan · Answer

No. that is not the answer.

use a calc to solve the right part.

anonymous · Answer

oh, K.

anonymous · Answer

@luisrock2008 Can you continue?

anonymous · Answer

not really

anonymous · Answer

Plug ln4/ ln 12 into your calculator,
then divide the result for 3 to get x value.

anonymous · Answer

You mean ln 12 / ln 4

anonymous · Answer

@nbouscal, thanks, I'm about to fix it :)

anonymous · Answer

why ln

anonymous · Answer

That's how you change the base!

anonymous · Answer

$$
\begin{align}

&\text{If}&y&=\log_ax,\
&\text{then}&x&=a^y=e^{y\log a},\
&\text{so}&\log x &=y\log a,\
&\text{or}&y&=\frac{\log x}{\log a}.\
&\text{In other words,}\
&&\log_a x&=\frac{\log x}{\log a}.

\end{align}
$$

anonymous · Answer

all this is confusing, is there an equation I can use on any problems like this

anonymous · Answer

That is the equation you can use, but you want to learn why the equation works. Revisit the definitions of the exponential and logarithmic functions if necessary.

anonymous · Answer

Is there any website or youtube videos that can explain this all to me step by step.

anonymous · Answer

I'm sure Khan has some good videos on it, khanacademy.com