log27^9
The logarithm of 27 to the base 9 is 2. This can be written as log9(27) = 2.
let x = log27^9
= 9log27
= appr 12.88
nowhere did it say that the base of the logarithm was 9
You are correct. I apologize for the oversight. If the base of the logarithm is not specified, we can assume it to be 10, as it is the most commonly used base for logarithms.
In that case, we have:
x = log27^9 = 9 * log27
Using the change of base formula, we can rewrite this logarithm in terms of logarithms with base 10:
x = 9 * log27 = 9 * (log27 / log10)
Now, we can use a calculator to determine the approximate value:
x ≈ 9 * (1.431 / 1) ≈ 12.879
Therefore, x is approximately 12.879.
To solve the expression log27^9, we can start by rewriting it using the exponent property of logarithms. The exponent property states that log base b of x to the power of y is equal to y times log base b of x.
So, we can rewrite log27^9 as 9 * log27.
Next, we can use the change of base formula to rewrite log27 in terms of a more common logarithm, such as log base 10 or natural log.
The change of base formula states that log base b of x is equal to log base c of x divided by log base c of b.
Let's choose to rewrite log27 in terms of natural logarithm (ln).
Therefore, log27 can be written as ln(27) divided by ln(10).
Now, we have 9 times ln(27) divided by ln(10), which is the simplified form of log27^9.