SOLUTION: how to solve for a subscript

Question 398807: how to solve for a subscript
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Short answer: You don't.

Subscripts are not often solved for unless you are working with sequences and/or series. Since you posted this under "Logarithms" I assume that this is not the case.

Perhaps you are thinking of bases of logarithms. They look like subscripts. For example:

To solve for x where x is the base of a logarithm, you want the equation to be in a form like:
log(expression) = other-expression
If the equation is not in this form, then use Algebra and/or the properties of logarithms to transform the equation so it looks like the form above.

Once the equation is in this form, then rewrite the equation in exponential form. In general, is equivalent to .

Once the equation is in exponential form the variable, which was in the base of the logarithm, is now a base with an exponent. This equation should be solvable.

The example above, , is already in the desired form. So we can proceed to rewriting the equation in exponential form:

To solve this equation we just find the cube root of each side:

which simplifies to:

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