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5.20 = 1.125^x

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2 Answers

To solve this, you must work backwards and deal with logarithms.
 
5.20 = 1.126^x
 
log (5.20) = x log 1.125
 
x = (log 5.20)/(log 1.125)
 
x = 13.997...rounding to 14
The First step to this problem is recognizing what you wish to find: that is the value of x. Then realize that every other part of the equation is a constant non x value.
 
The next is to recall what properties you can use to manipulate the equation.
 
Looking at this equation, with our variable as an exponent leads me to think of using the properties of logarithms:  lnx^y =ylnx
 
 
5.20 = 1.125^x
 
So the first thing I do is take the natural log of both sides:
 
ln5.2 =ln1.125^x
 
Does this form look familiar?
 
ln5.2= xln1.125
 
From this point it is a simple algebra equation and we solve for x
 
ln5.2/ln1.125=x
 
Solving from here gets you a numerical value of x≅13.9974200563
Plugging back in your original equation leaves you with the statement to test your answer
 
5.20=1.125^13.9974200563