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

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3 Answers
Dec 31, 2017

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

Explanation:

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.

Dec 31, 2017

C or may be A

Explanation:

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

Dec 31, 2017

Answer A

Explanation:

My answer was incorrect.

The correct answer was written very well by Alvin L.