# exponential equations

• Dec 1st 2009, 07:11 AM
extraordinarymachine
exponential equations
help please, i'm not sure how to solve this question. i know i need to use change of base, but i'm still confused.

solve equation, check for extraneous roots

2^x + 12(2)^-x = 7
• Dec 1st 2009, 07:35 AM
Hello extraordinarymachine
Quote:

Originally Posted by extraordinarymachine
help please, i'm not sure how to solve this question. i know i need to use change of base, but i'm still confused.

solve equation, check for extraneous roots

2^x + 12(2)^-x = 7

Multiply both sides by \$\displaystyle 2^x\$ and re-arrange:
\$\displaystyle (2^x)^2-7.2^x+12=0\$

\$\displaystyle \Rightarrow (2^x-3)(2^x-4)=0\$
Can you complete it now?

• Dec 1st 2009, 08:56 AM
mrmohamed
Quote:

Originally Posted by extraordinarymachine
help please, i'm not sure how to solve this question. i know i need to use change of base, but i'm still confused.

Quote:

Originally Posted by extraordinarymachine

solve equation, check for extraneous roots

2^x + 12(2)^-x = 7