# All help is GREATLY appreciated!!! :)

• Nov 6th 2008, 05:40 PM
Alesa'7
All help is GREATLY appreciated!!! :)
Solve for x to eight decimal places if

2^(2x – 1) = 3^(x-2)

back into original and show that it
will make each side equal.
• Nov 6th 2008, 05:42 PM
vincisonfire
\$\displaystyle 2(2x – 1) = 3(x-2)\$
\$\displaystyle 4x – 2 = 3x-6\$
\$\displaystyle x = -4\$
• Nov 6th 2008, 05:52 PM
Alesa'7
Oh I am sorry those numbers in parenthesis are suppost to be exponets (2x-1) and (x-2) are exponets, i am so sry.. :(
• Nov 6th 2008, 06:24 PM
mr fantastic
Quote:

Originally Posted by Alesa'7
Oh I am sorry those numbers in parenthesis are suppost to be exponets (2x-1) and (x-2) are exponets, i am so sry.. :(

\$\displaystyle 2^{2x-1} = 3^{x-2} \Rightarrow \log_{10} 2^{2x-1} = \log_{10} 3^{x-2} \Rightarrow (2x - 1) \log_{10} 2 = (x - 2) \log_{10} 3\$.

This has the form \$\displaystyle a(2x-1) = b(x - 2)\$. Expand and make x the subject. Then use a calculator to get the required approximate value.
• Nov 6th 2008, 06:40 PM
Alesa'7