Which logarithmic graph can be used to approximate the value of y in the equation 5^y = 12?

Question

janu16 · Answer

.

satellite73 · Answer

$$5^y=12\iff \log_5(12)=y$$

janu16 · Answer

@satellite73 ik tht part but how d i graph it?

janu16 · Answer

these are the options

mathmate · Answer

I assume you have a choice of different graphs.

The graph you posted passes through the points (12,1), (1,0) which therefore is a graph of $y=log_{12}(x)$.  Recall that $log_a(1)=0$ and $log_a(a)=1$.

Based on the above, choose the appropriate graph and post it for confirmation, based on 
$y=log_5(12) $

janu16 · Answer

ya i posted all of them above

mathmate · Answer

What I meant is to post the answer that you choose.

janu16 · Answer

when i solved y=log5(12) i got 1.543 so am i looking for that answer on the graph?

janu16 · Answer

@mathmate

mathmate · Answer

That's one way to do it, and it will give you the correct choice.  But the idea of the question is to choose the graph to estimate y in 5^y=12.

Recall that $log_a(1)=0$ and $log_a(a)=1$.
You would also get the same answer choice (graph) if you look for the graph which gives you $log(5)=1$, in which case it will be the right graph to use.  $Then$ you use the graph to estimate y=$log_5(12)$.

janu16 · Answer

is it the first one?

janu16 · Answer

@mathmate

mathmate · Answer

Reread what I just posted, and please explain why you chose the first one!

janu16 · Answer

because the first one passes through 12,1 thats why i picked it

mathmate · Answer

If it passes through (12,1), what is the base of the log function?

mathmate · Answer

Recall that $log_a(a)=1$!  Here you're looking at base=5.

janu16 · Answer

yea the base is 5

mathmate · Answer

if log(12)=1, the log graph has base equal to 12!

janu16 · Answer

yes so is it the last one ?

janu16 · Answer

@mathmate

mathmate · Answer

Well, I have not seen much effort on  your part, but I'll explain below and let you judge for yourself.
|dw:1463741046676:dw|
A typical log function (to base a) has a graph shown above, y=$log_a(x)$
There is a vertical asymptote towards -inf when x=0, so log(0) is undefined.
The graph is increasing for all values of x>0.
For ANY base a >0, the graph of y=$log_a(x)$ crosses the x-axis at x=1, i.e.
$log_a(1)=0$ for any a.
Also, for ANY base a>0, the graph of y=$log_a(x)$ crosses the line y=1 at x=a, i.e. 
$log_a(a)=1$.
The question is hinged upon the application of the last statement to locate the correct graph where a=5, which means that we are looking for the graph in which $log_5(5)=1$.
Now can you double check your answer with the last statement?

mathmate · Answer

|dw:1463741524273:dw|
Look for the graph where a=5 and decide if you have the right choice.