SOLUTION: solve equation for x=log11 1331

Question 74190: solve equation for x=log11 1331
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
I think what you are expressing is x equals the log to the base 11 of 1331.
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This can be rewritten in exponential form as:
.

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Now you can take the log to the base 10 of both sides to get:
.

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By the rules of logs the exponent x comes out as the multiplier of log 11 to give
.

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Now you can use your calculator in log to the base 10 mode to get that log 11 = 1.041392685.
Similarly you can use your calculator in log to the base 10 mode to find that log 1331 =
3.124178055.
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Substitute these two values into our equation to get:
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Now solve for x by dividing both sides by 1.041392685 to get:
.

.
So the answer to this problem is x = 3.
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Because the values are relatively small, when you got to the exponential form of:
.

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You could have just plugged values in for x until you got to but that
is just a "test taking" trick. The rigorous way to do it is using the procedures above.
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Hope this helps you to see your way through this problem. It has some good practice
with working with logs.

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