Evaluate log(base 3) 314

Round your answer to four decimals. 

Expert Answers

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Step 1:  Rewrite as 3^x = 314

Step 2:  Then, use Laws of Logs to write as follows:

             x log 3 = log 314

Step 3:  Use change of base rule

Divide both sides of the equation by log 3.

      x (log 3/log3) = log 314/log 3

The answer is 5.2333.

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To evaluate `log_3 314` , use the formula for change of base of logarithms:

`log_b a = (log_c a)/(log_c b)`

Then the given logarithm can be evaluated as

`log_3 314 = (ln 314)/(ln_3)` (ln is the natural logarithm, or logarithm with the base e). Natural logarithms can be found using a calculator.

`log_3 314 = 5.74939/1.09861 =5.2333 `

The value of the given logarithm rounded to 4 decimal places is 5.2333.

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