Solving the Equation
By: Lindsey P and Jayden F
Solving the equation

To solve exponential equations without logarithms, you need to have equations
with comparable exponential expressions on either side of the "equals" sign, so
you can compare the powers and solve. In other words, you have to have "(some
base) to (some power) equals (the same base) to (some other power)", where you
set the two powers equal to each other, and solve the resulting equation.
(http://www.purplemath.com/modules/solvexpo.htm)
Example
 For example:
 Solve 5x = 53.
 Since the bases ("5" in each case) are the same, then the
only way the two expressions could be equal is for the
powers also to be the same. That is:
 x=3
 This solution demonstrates how this entire class of
equation is solved: if the bases are the same, then the
powers must also be the same, in order for the two sides of
the equation to be equal to each other. Since the powers
must be the same, then you can set the two powers equal
to each other, and solve the resulting equation.
 (http://www.purplemath.com/modules/solvexpo.htm)
A Non Example
 A Non example:
 Solve 5x=53.
 NOT making the bases or the powers the
same.
A way to remember
 Do unto one that you do to the other, or
balance the two sides.