Question

What is the solution of the equation 3^x=12? Round your answer to the nearest ten-thousandth.

A) 0.4421

B) 0.4771

C) 0.5149

D) 2.2619

Answer 1

The answer is D.) 2.2619.

Answer 2

Hey!


Okay, so if
`f(x)` equals
`g(x)`, then
`In(f(x))` equals
`In(g(x))`. So, we'll plug in the numbers into this 'equation' we have now.


`In(3^(x) ) = In(12 )`

And now we'll apply this log rule →
`log_(a) (x^(b) ) = b * log_(a) (x)`


`In(3^(x) )=xIn(3) \\ xIn(3)=In(12)`

Now we have to solve
`In(3^(x) )=xIn(3) \\ xIn(3)=In(12)`. To do that, we'll divide both sides of the equation by
`In(3)`.


`(xIn(3))/(In3) = (In(12))/(In(3))`

Now we simplify


`x = (In(12))/(In(3))`

So, this means the equation
`3^(x) =12` solved is
`x = (In(12))/(In(3))` or 2.2619.

Hope this helps!


- Lindsey Frazier ♥