SOLUTION: log(n)39870=28

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Question 348510: log(n)39870=28
Answer by jsmallt9(3758)   (Show Source): You can put this solution on YOUR website!
An equation of this form:
log(expression) = 0ther-expression
is usually solved by rewriting it in exponential form. In general, is equivalent to . In your case:

is equivalent to:


To solve this equation we want to end up with an equation of the form:
n = expression
The "n" above has no visible exponent. Nevertheless the "n" does have an exponent. Any "invisible" exponent is always understood to be a 1. So, even though we don't usually write it this way, what we are looking for is:
= experession.

So how to we change the that we have into the that we want? Thinking through our rules for exponents and thinking about when we get a 1 as an answer, we may be able to realize that
So in order to change the to we will need to raise it to the reciprocal of 28, 1/28, power. And if we raise the left side to the 1/28 power, we must also raise the right side to the same power:

which simplifies to

which, in radical form, is

This is an exact expression for the solution. If you need a decimal approximation, then we can use out calclators. If your calculator has buttons for parentheses, "(" and ")", then you can just type:
39870^(1/28)
If your calculator does not have buttons for parentheses, then first calculate 1/28 (approximately 0.0357142857) and use this decimal for the exponent:
39870^0.0357142857
Either way you should get appoximately 1.46.
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