ure, in the first example, I used the property logb(x^n) = nlogb(x) to find the logarithm of 27 to base 3. The property states that the logarithm of a number x raised to a power n to base b is equal to n multiplied by the logarithm of x to base b.
Here’s the step-by-step breakdown of the calculation:
- We are trying to find the logarithm of 27 to base 3, so we start by using the fact that 27 = 3^3.
- We substitute this into the logarithm: log3(3^3)
- We then use the property logb(x^n) = nlogb(x) to simplify the equation: 3log3(3)
- Next we need to find log3(3) which is equal to 2 because 3^2=9
- Now we can substitute this into our equation: 3*2
- So the final result is log3(27) = 32 = 6*
So, the logarithm of 27 to base 3 is 6. This means that 3^6 = 729, which is equal to 27.
Hope that makes it more clear, please let me know if there’s anything else I can help you with.
why 3^6 = 27
I apologize for the confusion, in the last statement I said that 3^6 = 729 which is not correct, the correct statement is 3^3 = 27.
The reason is that when we raise a number to a certain power, for example 3^3, we are multiplying 3 by itself 3 times. So, 3^3 = 3 * 3 * 3 = 27.
In other words, the exponent (3) tells us how many times we are multiplying the base (3) by itself. So, 3^3 means 3 multiplied by itself 3 times.
It’s a common mistake and I apologize for any confusion caused. Thank you for bringing this to my attention.