Evaluate the expression below
log 243
9
log9243 = log3243/log39
= 5/2
Think of it like this. Since 9 = 3^2, 9^n = (3^2)^n = 3^2n
That is, the power of 3 will be twice the power of 9.
Logs work the same way. The power of 9 needed to get to n is half the power of 3. Since log9n is the power of 9 needed to produce n, it will be half the power of 3 needed.
To evaluate the given expression "log 243 / 9":
Step 1: Understand the meaning of log
In mathematics, "log" is the logarithm function that calculates the exponent to which a given base must be raised to obtain a certain number. In this case, we are looking for the logarithm of 243 divided by 9.
Step 2: Determine the base
The base of the logarithm is not specified, so we will assume it is base 10, as log base 10 (log10) is commonly used.
Step 3: Substitute the values into the expression
Now we can substitute the values into the expression "log 243 / 9":
log10 (243) / 9
Step 4: Use a calculator or logarithm table
To evaluate the expression, we need to calculate log10 (243) and then divide the result by 9.
Using a calculator, the value of log10 (243) is approximately 2.385
So, the expression can be simplified as:
2.385 / 9
Step 5: Calculate the final value
Now, divide 2.385 by 9 to get the final value:
2.385 / 9 = approximately 0.265
Therefore, the evaluated value of the expression "log 243 / 9" is approximately 0.265