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 July 4th, 2015, 02:28 PM #1 Newbie   Joined: Jul 2015 From: California Posts: 5 Thanks: 0 Solve for X Can someone help show the process? Solve for X 3^(5x+2) = 27^(x-4) Note: the answer is x = -7
July 4th, 2015, 03:05 PM   #2
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Quote:
 Originally Posted by jimbodot Can someone help show the process? Solve for X 3^(5x+2) = 27^(x-4) Note: the answer is x = -7
$\displaystyle 3^{5x+2} = (3^3)^{x-4}$

use the appropriate rule re: exponents on the right side of the equation and match up the equal exponents ...

 July 24th, 2015, 05:44 PM #3 Newbie   Joined: Jul 2015 From: Serbia Posts: 8 Thanks: 1 $\begin{array}{l} {3^{5x + 2}} = {27^{x - 4}}\\ {3^{5x + 2}} = {\left( {{3^3}} \right)^{x - 4}}\\ {3^{5x + 2}} = {3^{3\left( {x - 4} \right)}}\\ {3^{5x + 2}} = {3^{3x - 12}}\\ 5x + 2 = 3x - 12\\ 5x - 3x = - 12 - 2\\ 2x = - 14\\ x = - \frac{{14}}{2} = - 7 \end{array}$
 July 24th, 2015, 07:42 PM #4 Senior Member   Joined: May 2015 From: Varanasi Posts: 110 Thanks: 5 Math Focus: Calculus The equation will simplify to 5x+2=3x-12 on solving you will get, x=-7

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