Evaluate log(base 3) 314 Round your answer to four decimals.
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.
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.
The solution is 5.2333 (4 d. p.).
Log(base 3) 314 = 5.2333
(Found using online logarithm calculator)
We could guess that the answer would be approximately more than 5, because 3^5 = 243 and 3^6 = 729.
We need to find log(base 3) 314 and round to 4 decimal places.
A standard graphing calculator can do this automatically but lets say you don't have one. We can just use the change of base formula which is super easy:
Your problem becomes : log314 / log3
which is 5.2333