# INDICES

• Oct 28th 2008, 11:16 AM
abey_27
INDICES
what is 32^x = 2 ?

what is x? thanks
• Oct 28th 2008, 11:19 AM
earboth
Quote:

Originally Posted by abey_27
what is 32^x = 2 ?

what is x? thanks

Re-write the equation:

\$\displaystyle 32^x=2~\implies~(2^5)^x=2^1\$

Now solve for x.
• Oct 28th 2008, 11:28 AM
abey_27
cheers earboth but i still dont really understand how to find x. i understand what you have done but there onwards not too sure. could you please tell me how to progress from your last comment. thank you

Quote:

Originally Posted by earboth
Re-write the equation:

\$\displaystyle 32^x=2~\implies~(2^5)^x=2^1\$

Now solve for x.

• Oct 28th 2008, 11:30 AM
earboth
Quote:

Originally Posted by abey_27
cheers earboth but i still dont really understand how to find x. i understand what you have done but there onwards not too sure. could you please tell me how to progress from your last comment. thank you

Since the bases of the 2 expressions are equal the exponents must be equal too:

\$\displaystyle
32^x=2~\implies~(2^5)^x=2^1~\implies~2^{5x} = 2^1~\implies~ 5x=1~\implies~x=\dfrac15
\$
• Oct 28th 2008, 11:33 AM
thegarden
You then equate the indices,
so 5x=1
so x=1/5
• Oct 28th 2008, 11:34 AM
thegarden
lol earboth got there before me
• Oct 28th 2008, 11:34 AM
abey_27
lol cheers man