SOLUTION: If I'm given 729 = 3^?, Is there an easy way to calculate what the exponent is without dividing backwards? How to punch in to a calculator...

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Question 1010135: If I'm given 729 = 3^?,
Is there an easy way to calculate what the exponent is without dividing backwards?
How to punch in to a calculator...
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618)   (Show Source): You can put this solution on YOUR website!
Three-digit number, so factorization should be an easy chore. Look to find that 7+2+9=18, a multiple of 3, so try to completely factorize...


You should see what the exponent is on the base of 3.

If it is the calculator skill you want, then that's a little different. No key on a calculator (scientific nor graphical) for this.

Something else you might try is start with 3, the base, and find successive powers of 3. You "might" get 729 or something near to it. If not, then you may want to learn about logarithms (but that is not needed for the example you asked).
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

If I'm given 729 = 3^?,
Is there an easy way to calculate what the exponent is without dividing backwards?
How to punch in to a calculator...
Let exponent be a

Then we get: 

One way is to convert to logs, as follows:



 ------ Applying change of base

Punching that in the calculator will give: , the exponent 

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