Which way is correct

[Timcago]

Solve the following equation for x.

log(base 9)^(log(base 5)^x)=1/2

my first strategy:

1. put it in standard form.

-> 9^(1/2)=log(base 5)^x

-> 3=log(base 5)^x

2. put in standard form again

->5^3=x

-> x=125


Second strategy:

1. put it in standard form.

-> 9^(1/2)=log(base 5)^x

-> 3=log(base 5)^x

2. take the natural log of both sides

ln(3) = e(log(base 5)^x)

3. according to a rule e(log(base 5)^x) equals x, right?

e(3)=x


Why doesnt the second way work give me the same answer. Which answer is correct.

 

[tkhunny]

2. take the natural log of both sides

ln(3) = e(log(base 5)^x)

Where did 'e' come from?

ln(3) = ln[(log(base 5)^x)]

And you pretty much just made a mess.

Golden Nugget of Truth: Unique Answers do not care how you find them. Any way you solve it consistently and accurately is fine. Some variations may be harder to program or explain, but that makes them no less valid.

Your notation is really hard to read. Figure out superscripts and subscripts, or maybe use the LaTeX aides under "Forum Help" at the top of the page.