Question

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

Answer 1

`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.

Answer 2

C or may be A

Explanation:

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

Answer 3

Answer A

Explanation:

My answer was incorrect.

The correct answer was written very well by Alvin L.