If #y=ab^x# what is x ?

Question

Caleb Alexander · Accepted Answer

#x=ln(y \/ a)/ln(b)#

First we divide both sides by #a# to get: #y/a=b^x#

To crack this apart further, we could take #log_b# on both sides, but none of the alternatives involve #log_b#. I will instead use #ln# on both sides and then take advantage of some log properties. #ln(y/a)=ln(b^x)#

Now we can use the logarithm properties to move the #x# power out the front of the logarithm: #ln(y/a)=xln(b)#

Now we divide both sides by #ln(b)#: #ln(y/a)/ln(b)=x#

This is the same as alternative A, which is the correct answer.

Ariana Alvarez · Answer

Answer A

My answer was incorrect. The correct answer was written very well by Alvin L.

Lincoln Anderson · Answer

C or may be A

we know that if #a=b^c#
then
#c=lna/lnb#

similarly
if #y=ab^x#
then
#x=ln y/ln ab#

that's the answer its C
. but wait , there could be an alternate solution , may be it would be more correct than it is!
i assumed that the question was
#(ab)^x=y #
it could be
#a xx b^x=y#
in this case
first divide both sides by a that makes
#b^x=y/a#
on applying same principles we'd applied earlier
we get answer
#ln (y/a)/ln b# that's part A