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July 4th, 2015, 01:28 PM   #1
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Solve for X

Can someone help show the process?

Solve for X

3^(5x+2) = 27^(x-4)

Note: the answer is x = -7
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July 4th, 2015, 02:05 PM   #2
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Quote:
Originally Posted by jimbodot View Post
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 ...
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July 24th, 2015, 04:44 PM   #3
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\[\begin{array}{l}
{3^{5x + 2}} = {27^{x - 4}}\\
{3^{5x + 2}} = {\left( {{3^3}} \right)^{x - 4}}\\
{3^{5x + 2}} = {3^{3\left( {x - 4} \right)}}\\
{3^{5x + 2}} = {3^{3x - 12}}\\
5x + 2 = 3x - 12\\
5x - 3x = - 12 - 2\\
2x = - 14\\
x = - \frac{{14}}{2} = - 7
\end{array}\]
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July 24th, 2015, 06:42 PM   #4
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The equation will simplify to 5x+2=3x-12
on solving you will get, x=-7
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