How to Solve aB=a^B in Neutral Operations Using Algebra
Create a new Excel worksheet and enter into cell A1 a*b = a^b, where "^" is Excel's symbol for exponentiation., Substitute in trial values for b in order to obtain the value of a; Let b = 10., Test the hypothesis of the original formula, i.e.
Step-by-Step Guide
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Step 1: Create a new Excel worksheet and enter into cell A1 a*b = a^b
Enter into cell A2 ab/a = (a^b)/a Enter into cell A3 b = a^(b-1) Enter into cell A4 b^(1/(b-1)) = a; a has now been isolated and defined in terms of b and 1 but b may not = 1 lest division by 0 result in the denominator.
The simple algebra is complete. -
Step 2: where "^" is Excel's symbol for exponentiation.
Enter in cell C1 ="a=b^(1/(b-1))" Enter into cell F1 the word "Var b" for variable b.
Enter into cell F2 the value
10.
Do MenuCommand Insert Name DefineName "Var" to cell F2.
Enter into cell C2 the formula, without quotes, "=Var^(1/(Var-1))" Copy the value in cell C2 and do Edit Paste Special Value into cell C3.
The value you obtain should be
1.29154966501488 , that a*b = a^b:
Enter a*b into cell F3 Enter the formula, without quotes, "=C2*Var" into cell F4.
Enter a^b into cell F5 Enter the formula, without quotes, "=C2^Var" into cell F6.
Enter the formula, without quotes, "=F4-F6" into F7.
The result should be
0.
Done, because C2*Var = C2^Var, and the difference in F7 is 0! -
Step 3: Substitute in trial values for b in order to obtain the value of a; Let b = 10.
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Step 4: Test the hypothesis of the original formula
Detailed Guide
Enter into cell A2 ab/a = (a^b)/a Enter into cell A3 b = a^(b-1) Enter into cell A4 b^(1/(b-1)) = a; a has now been isolated and defined in terms of b and 1 but b may not = 1 lest division by 0 result in the denominator.
The simple algebra is complete.
Enter in cell C1 ="a=b^(1/(b-1))" Enter into cell F1 the word "Var b" for variable b.
Enter into cell F2 the value
10.
Do MenuCommand Insert Name DefineName "Var" to cell F2.
Enter into cell C2 the formula, without quotes, "=Var^(1/(Var-1))" Copy the value in cell C2 and do Edit Paste Special Value into cell C3.
The value you obtain should be
1.29154966501488 , that a*b = a^b:
Enter a*b into cell F3 Enter the formula, without quotes, "=C2*Var" into cell F4.
Enter a^b into cell F5 Enter the formula, without quotes, "=C2^Var" into cell F6.
Enter the formula, without quotes, "=F4-F6" into F7.
The result should be
0.
Done, because C2*Var = C2^Var, and the difference in F7 is 0!
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